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Mirrors > Home > MPE Home > Th. List > supisolem | Structured version Visualization version Unicode version |
Description: Lemma for supiso 8381. (Contributed by Mario Carneiro, 24-Dec-2016.) |
Ref | Expression |
---|---|
supiso.1 | |
supiso.2 |
Ref | Expression |
---|---|
supisolem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | supiso.1 | . . 3 | |
2 | supiso.2 | . . 3 | |
3 | 1, 2 | jca 554 | . 2 |
4 | simpll 790 | . . . . . . . 8 | |
5 | 4 | adantr 481 | . . . . . . 7 |
6 | simplr 792 | . . . . . . 7 | |
7 | simplr 792 | . . . . . . . 8 | |
8 | 7 | sselda 3603 | . . . . . . 7 |
9 | isorel 6576 | . . . . . . 7 | |
10 | 5, 6, 8, 9 | syl12anc 1324 | . . . . . 6 |
11 | 10 | notbid 308 | . . . . 5 |
12 | 11 | ralbidva 2985 | . . . 4 |
13 | isof1o 6573 | . . . . . . 7 | |
14 | 4, 13 | syl 17 | . . . . . 6 |
15 | f1ofn 6138 | . . . . . 6 | |
16 | 14, 15 | syl 17 | . . . . 5 |
17 | breq2 4657 | . . . . . . 7 | |
18 | 17 | notbid 308 | . . . . . 6 |
19 | 18 | ralima 6498 | . . . . 5 |
20 | 16, 7, 19 | syl2anc 693 | . . . 4 |
21 | 12, 20 | bitr4d 271 | . . 3 |
22 | 4 | adantr 481 | . . . . . . 7 |
23 | simpr 477 | . . . . . . 7 | |
24 | simplr 792 | . . . . . . 7 | |
25 | isorel 6576 | . . . . . . 7 | |
26 | 22, 23, 24, 25 | syl12anc 1324 | . . . . . 6 |
27 | 22 | adantr 481 | . . . . . . . . 9 |
28 | simplr 792 | . . . . . . . . 9 | |
29 | 7 | adantr 481 | . . . . . . . . . 10 |
30 | 29 | sselda 3603 | . . . . . . . . 9 |
31 | isorel 6576 | . . . . . . . . 9 | |
32 | 27, 28, 30, 31 | syl12anc 1324 | . . . . . . . 8 |
33 | 32 | rexbidva 3049 | . . . . . . 7 |
34 | 16 | adantr 481 | . . . . . . . 8 |
35 | breq2 4657 | . . . . . . . . 9 | |
36 | 35 | rexima 6497 | . . . . . . . 8 |
37 | 34, 29, 36 | syl2anc 693 | . . . . . . 7 |
38 | 33, 37 | bitr4d 271 | . . . . . 6 |
39 | 26, 38 | imbi12d 334 | . . . . 5 |
40 | 39 | ralbidva 2985 | . . . 4 |
41 | f1ofo 6144 | . . . . 5 | |
42 | breq1 4656 | . . . . . . 7 | |
43 | breq1 4656 | . . . . . . . 8 | |
44 | 43 | rexbidv 3052 | . . . . . . 7 |
45 | 42, 44 | imbi12d 334 | . . . . . 6 |
46 | 45 | cbvfo 6544 | . . . . 5 |
47 | 14, 41, 46 | 3syl 18 | . . . 4 |
48 | 40, 47 | bitrd 268 | . . 3 |
49 | 21, 48 | anbi12d 747 | . 2 |
50 | 3, 49 | sylan 488 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 wss 3574 class class class wbr 4653 cima 5117 wfn 5883 wfo 5886 wf1o 5887 cfv 5888 wiso 5889 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-isom 5897 |
This theorem is referenced by: supisoex 8380 supiso 8381 |
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