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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj996 | 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 |
---|---|
bnj996.1 | |
bnj996.2 | |
bnj996.3 | |
bnj996.4 | |
bnj996.5 | |
bnj996.6 | |
bnj996.13 | |
bnj996.14 |
Ref | Expression |
---|---|
bnj996 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj996.4 | . . . . 5 | |
2 | bnj996.1 | . . . . . 6 | |
3 | bnj996.2 | . . . . . 6 | |
4 | bnj996.13 | . . . . . 6 | |
5 | bnj996.14 | . . . . . 6 | |
6 | bnj996.3 | . . . . . 6 | |
7 | 2, 3, 4, 5, 6 | bnj917 31004 | . . . . 5 |
8 | 1, 7 | bnj771 30834 | . . . 4 |
9 | 3anass 1042 | . . . . . 6 | |
10 | bnj996.6 | . . . . . . 7 | |
11 | 10 | anbi2i 730 | . . . . . 6 |
12 | 9, 11 | bitr4i 267 | . . . . 5 |
13 | 12 | 3exbii 1776 | . . . 4 |
14 | 8, 13 | sylib 208 | . . 3 |
15 | bnj996.5 | . . . . . . . . . 10 | |
16 | 6, 4, 15 | bnj986 31024 | . . . . . . . . 9 |
17 | 16 | ancli 574 | . . . . . . . 8 |
18 | 19.42vv 1920 | . . . . . . . 8 | |
19 | 17, 18 | sylibr 224 | . . . . . . 7 |
20 | 19 | anim1i 592 | . . . . . 6 |
21 | 19.41vv 1915 | . . . . . 6 | |
22 | 20, 21 | sylibr 224 | . . . . 5 |
23 | df-3an 1039 | . . . . . 6 | |
24 | 23 | 2exbii 1775 | . . . . 5 |
25 | 22, 24 | sylibr 224 | . . . 4 |
26 | 25 | 2eximi 1763 | . . 3 |
27 | 14, 26 | bnj593 30815 | . 2 |
28 | 19.37v 1910 | . . . . . . . . . 10 | |
29 | 28 | exbii 1774 | . . . . . . . . 9 |
30 | 29 | bnj132 30792 | . . . . . . . 8 |
31 | 30 | exbii 1774 | . . . . . . 7 |
32 | 31 | bnj132 30792 | . . . . . 6 |
33 | 32 | exbii 1774 | . . . . 5 |
34 | 33 | bnj132 30792 | . . . 4 |
35 | 34 | exbii 1774 | . . 3 |
36 | 35 | bnj132 30792 | . 2 |
37 | 27, 36 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wex 1704 wcel 1990 cab 2608 wral 2912 wrex 2913 cdif 3571 c0 3915 csn 4177 ciun 4520 csuc 5725 wfn 5883 cfv 5888 com 7065 w-bnj17 30752 c-bnj14 30754 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-fn 5891 df-om 7066 df-bnj17 30753 df-bnj18 30761 |
This theorem is referenced by: bnj1021 31034 |
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