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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj945 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj69 31078. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj945.1 |
Ref | Expression |
---|---|
bnj945 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fndm 5990 | . . . . . . 7 | |
2 | 1 | ad2antll 765 | . . . . . 6 |
3 | 2 | eleq2d 2687 | . . . . 5 |
4 | 3 | pm5.32i 669 | . . . 4 |
5 | bnj945.1 | . . . . . . . . 9 | |
6 | 5 | bnj941 30843 | . . . . . . . 8 |
7 | 6 | imp 445 | . . . . . . 7 |
8 | 7 | bnj930 30840 | . . . . . 6 |
9 | 5 | bnj931 30841 | . . . . . 6 |
10 | 8, 9 | jctir 561 | . . . . 5 |
11 | 10 | anim1i 592 | . . . 4 |
12 | 4, 11 | sylbir 225 | . . 3 |
13 | df-bnj17 30753 | . . . 4 | |
14 | 3ancomb 1047 | . . . . . 6 | |
15 | 3anass 1042 | . . . . . 6 | |
16 | 14, 15 | bitri 264 | . . . . 5 |
17 | 16 | anbi1i 731 | . . . 4 |
18 | 13, 17 | bitri 264 | . . 3 |
19 | df-3an 1039 | . . 3 | |
20 | 12, 18, 19 | 3imtr4i 281 | . 2 |
21 | funssfv 6209 | . 2 | |
22 | 20, 21 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 cvv 3200 cun 3572 wss 3574 csn 4177 cop 4183 cdm 5114 csuc 5725 wfun 5882 wfn 5883 cfv 5888 w-bnj17 30752 |
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 ax-reg 8497 |
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-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 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-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-res 5126 df-suc 5729 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-bnj17 30753 |
This theorem is referenced by: bnj966 31014 bnj967 31015 bnj1006 31029 |
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