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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1173 | 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 |
---|---|
bnj1173.3 | |
bnj1173.5 | |
bnj1173.9 | |
bnj1173.17 |
Ref | Expression |
---|---|
bnj1173 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1173.5 | . . 3 | |
2 | 3simpc 1060 | . . . 4 | |
3 | bnj1173.9 | . . . . . . 7 | |
4 | 3 | 3adant3 1081 | . . . . . 6 |
5 | bnj1173.17 | . . . . . . 7 | |
6 | 5 | 3adant3 1081 | . . . . . 6 |
7 | elin 3796 | . . . . . . . . 9 | |
8 | 7 | simplbi 476 | . . . . . . . 8 |
9 | bnj1173.3 | . . . . . . . 8 | |
10 | 8, 9 | eleq2s 2719 | . . . . . . 7 |
11 | 10 | 3ad2ant3 1084 | . . . . . 6 |
12 | pm3.21 464 | . . . . . 6 | |
13 | 4, 6, 11, 12 | syl3anc 1326 | . . . . 5 |
14 | bnj170 30764 | . . . . 5 | |
15 | 13, 14 | syl6ibr 242 | . . . 4 |
16 | 2, 15 | impbid2 216 | . . 3 |
17 | 1, 16 | syl5bb 272 | . 2 |
18 | bnj1147 31062 | . . . . 5 | |
19 | 18, 11 | bnj1213 30869 | . . . 4 |
20 | 4, 19 | jca 554 | . . 3 |
21 | 20 | biantrurd 529 | . 2 |
22 | 17, 21 | bitr4d 271 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 cin 3573 w-bnj15 30758 c-bnj18 30760 |
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-8 1992 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-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 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-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-tr 4753 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-iota 5851 df-fn 5891 df-fv 5896 df-om 7066 df-bnj17 30753 df-bnj14 30755 df-bnj18 30761 |
This theorem is referenced by: bnj1190 31076 |
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