Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj969 | 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 |
---|---|
bnj969.1 | |
bnj969.2 | |
bnj969.3 | |
bnj969.10 | |
bnj969.12 | |
bnj969.14 | |
bnj969.15 |
Ref | Expression |
---|---|
bnj969 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 473 | . . . 4 | |
2 | bnj667 30822 | . . . . . . 7 | |
3 | bnj969.3 | . . . . . . 7 | |
4 | bnj969.14 | . . . . . . 7 | |
5 | 2, 3, 4 | 3imtr4i 281 | . . . . . 6 |
6 | 5 | 3ad2ant1 1082 | . . . . 5 |
7 | 6 | adantl 482 | . . . 4 |
8 | 3 | bnj1232 30874 | . . . . . . 7 |
9 | vex 3203 | . . . . . . . 8 | |
10 | 9 | bnj216 30800 | . . . . . . 7 |
11 | id 22 | . . . . . . 7 | |
12 | 8, 10, 11 | 3anim123i 1247 | . . . . . 6 |
13 | bnj969.15 | . . . . . . 7 | |
14 | 3ancomb 1047 | . . . . . . 7 | |
15 | 13, 14 | bitri 264 | . . . . . 6 |
16 | 12, 15 | sylibr 224 | . . . . 5 |
17 | 16 | adantl 482 | . . . 4 |
18 | 1, 7, 17 | jca32 558 | . . 3 |
19 | bnj256 30772 | . . 3 | |
20 | 18, 19 | sylibr 224 | . 2 |
21 | bnj969.12 | . . 3 | |
22 | bnj969.10 | . . . 4 | |
23 | bnj969.1 | . . . 4 | |
24 | bnj969.2 | . . . 4 | |
25 | 22, 4, 13, 23, 24 | bnj938 31007 | . . 3 |
26 | 21, 25 | syl5eqel 2705 | . 2 |
27 | 20, 26 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 wral 2912 cvv 3200 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 |
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-rep 4771 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-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 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-mpt 4730 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 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-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 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-om 7066 df-bnj17 30753 df-bnj14 30755 df-bnj13 30757 df-bnj15 30759 |
This theorem is referenced by: bnj910 31018 bnj1006 31029 |
Copyright terms: Public domain | W3C validator |