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Mirrors > Home > NFE Home > Th. List > fvopab4t | Unicode version |
Description: Closed theorem form of fvopab4 5389. (Contributed by set.mm contributors, 21-Feb-2013.) |
Ref | Expression |
---|---|
fvopab4t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2867 | . . 3 | |
2 | 1 | anim2i 552 | . 2 |
3 | funopab4 5141 | . . . 4 | |
4 | simp2 956 | . . . . . 6 | |
5 | 4 | 19.21bi 1758 | . . . . 5 |
6 | 5 | funeqd 5129 | . . . 4 |
7 | 3, 6 | mpbiri 224 | . . 3 |
8 | simp3l 983 | . . . . 5 | |
9 | eqidd 2354 | . . . . 5 | |
10 | eleq1 2413 | . . . . . . . . . . 11 | |
11 | eqeq2 2362 | . . . . . . . . . . 11 | |
12 | 10, 11 | bi2anan9 843 | . . . . . . . . . 10 |
13 | 12 | ex 423 | . . . . . . . . 9 |
14 | 13 | a2i 12 | . . . . . . . 8 |
15 | 14 | 2alimi 1560 | . . . . . . 7 |
16 | 15 | 3ad2ant1 976 | . . . . . 6 |
17 | eqeq1 2359 | . . . . . . . . 9 | |
18 | 17 | anbi2d 684 | . . . . . . . 8 |
19 | 18 | gen2 1547 | . . . . . . 7 |
20 | 19 | a1i 10 | . . . . . 6 |
21 | simp3 957 | . . . . . 6 | |
22 | opelopabt 4699 | . . . . . 6 | |
23 | 16, 20, 21, 22 | syl3anc 1182 | . . . . 5 |
24 | 8, 9, 23 | mpbir2and 888 | . . . 4 |
25 | 24, 5 | eleqtrrd 2430 | . . 3 |
26 | funopfv 5357 | . . 3 | |
27 | 7, 25, 26 | sylc 56 | . 2 |
28 | 2, 27 | syl3an3 1217 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 w3a 934 wal 1540 wceq 1642 wcel 1710 cvv 2859 cop 4561 copab 4622 wfun 4775 cfv 4781 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-13 1712 ax-14 1714 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3or 935 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-reu 2621 df-rmo 2622 df-rab 2623 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-pss 3261 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-idk 4195 df-iota 4339 df-0c 4377 df-addc 4378 df-nnc 4379 df-fin 4380 df-lefin 4440 df-ltfin 4441 df-ncfin 4442 df-tfin 4443 df-evenfin 4444 df-oddfin 4445 df-sfin 4446 df-spfin 4447 df-phi 4565 df-op 4566 df-proj1 4567 df-proj2 4568 df-opab 4623 df-br 4640 df-co 4726 df-ima 4727 df-id 4767 df-cnv 4785 df-rn 4786 df-dm 4787 df-fun 4789 df-fv 4795 |
This theorem is referenced by: (None) |
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