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Theorem bnj1385 33326
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1385.1
bnj1385.2
bnj1385.3
bnj1385.4
bnj1385.5
bnj1385.6
bnj1385.7
Assertion
Ref Expression
bnj1385
Distinct variable groups:   ,,,   ,   ,   ,,,   ,
Allowed substitution hints:   (,,,)   (,,,)   ()   (,,)   (,,)   (,,)   (,,,)

Proof of Theorem bnj1385
StepHypRef Expression
1 nfv 1683 . . . . . . 7
2 bnj1385.4 . . . . . . . . . 10
32nfcii 2619 . . . . . . . . 9
43nfcri 2622 . . . . . . . 8
5 nfv 1683 . . . . . . . 8
64, 5nfim 1867 . . . . . . 7
7 eleq1 2539 . . . . . . . 8
8 funeq 5613 . . . . . . . 8
97, 8imbi12d 320 . . . . . . 7
101, 6, 9cbval 1994 . . . . . 6
11 df-ral 2822 . . . . . 6
12 df-ral 2822 . . . . . 6
1310, 11, 123bitr4i 277 . . . . 5
14 bnj1385.1 . . . . 5
15 bnj1385.5 . . . . 5
1613, 14, 153bitr4i 277 . . . 4
17 nfv 1683 . . . . . 6
18 nfv 1683 . . . . . . . 8
193, 18nfral 2853 . . . . . . 7
204, 19nfim 1867 . . . . . 6
21 dmeq 5209 . . . . . . . . . . . . 13
2221ineq1d 3704 . . . . . . . . . . . 12
23 bnj1385.2 . . . . . . . . . . . 12
24 bnj1385.6 . . . . . . . . . . . 12
2522, 23, 243eqtr4g 2533 . . . . . . . . . . 11
2625reseq2d 5279 . . . . . . . . . 10
27 reseq1 5273 . . . . . . . . . 10
2826, 27eqtrd 2508 . . . . . . . . 9
2925reseq2d 5279 . . . . . . . . 9
3028, 29eqeq12d 2489 . . . . . . . 8
3130ralbidv 2906 . . . . . . 7
327, 31imbi12d 320 . . . . . 6
3317, 20, 32cbval 1994 . . . . 5
34 df-ral 2822 . . . . 5
35 df-ral 2822 . . . . 5
3633, 34, 353bitr4i 277 . . . 4
3716, 36anbi12i 697 . . 3
38 bnj1385.3 . . 3
39 bnj1385.7 . . 3
4037, 38, 393bitr4i 277 . 2
4115, 24, 39bnj1383 33325 . 2
4240, 41sylbi 195 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1377   wceq 1379   wcel 1767  wral 2817   cin 3480  cuni 4251   cdm 5005   cres 5007   wfun 5588 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-iun 4333  df-br 4454  df-opab 4512  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-res 5017  df-iota 5557  df-fun 5596  df-fv 5602 This theorem is referenced by:  bnj1386  33327
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