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Mirrors > Home > MPE Home > Th. List > supisoex | Structured version Visualization version Unicode version |
Description: Lemma for supiso 8381. (Contributed by Mario Carneiro, 24-Dec-2016.) |
Ref | Expression |
---|---|
supiso.1 | |
supiso.2 | |
supisoex.3 |
Ref | Expression |
---|---|
supisoex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | supisoex.3 | . 2 | |
2 | supiso.1 | . . 3 | |
3 | supiso.2 | . . 3 | |
4 | simpl 473 | . . . . . 6 | |
5 | simpr 477 | . . . . . 6 | |
6 | 4, 5 | supisolem 8379 | . . . . 5 |
7 | isof1o 6573 | . . . . . . . 8 | |
8 | f1of 6137 | . . . . . . . 8 | |
9 | 4, 7, 8 | 3syl 18 | . . . . . . 7 |
10 | 9 | ffvelrnda 6359 | . . . . . 6 |
11 | breq1 4656 | . . . . . . . . . . 11 | |
12 | 11 | notbid 308 | . . . . . . . . . 10 |
13 | 12 | ralbidv 2986 | . . . . . . . . 9 |
14 | breq2 4657 | . . . . . . . . . . 11 | |
15 | 14 | imbi1d 331 | . . . . . . . . . 10 |
16 | 15 | ralbidv 2986 | . . . . . . . . 9 |
17 | 13, 16 | anbi12d 747 | . . . . . . . 8 |
18 | 17 | rspcev 3309 | . . . . . . 7 |
19 | 18 | ex 450 | . . . . . 6 |
20 | 10, 19 | syl 17 | . . . . 5 |
21 | 6, 20 | sylbid 230 | . . . 4 |
22 | 21 | rexlimdva 3031 | . . 3 |
23 | 2, 3, 22 | syl2anc 693 | . 2 |
24 | 1, 23 | mpd 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 wss 3574 class class class wbr 4653 cima 5117 wf 5884 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: (None) |
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