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Theorem ovmpt2dv 6434
 Description: Alternate deduction version of ovmpt2 6437, suitable for iteration. (Contributed by Mario Carneiro, 7-Jan-2017.)
Hypotheses
Ref Expression
ovmpt2df.1
ovmpt2df.2
ovmpt2df.3
ovmpt2df.4
Assertion
Ref Expression
ovmpt2dv
Distinct variable groups:   ,,   ,   ,,   ,,   ,,
Allowed substitution hints:   ()   (,)   (,)   (,)   (,)

Proof of Theorem ovmpt2dv
StepHypRef Expression
1 ovmpt2df.1 . 2
2 ovmpt2df.2 . 2
3 ovmpt2df.3 . 2
4 ovmpt2df.4 . 2
5 nfcv 2619 . 2
6 nfv 1708 . 2
7 nfcv 2619 . 2
8 nfv 1708 . 2
91, 2, 3, 4, 5, 6, 7, 8ovmpt2df 6433 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819  (class class class)co 6296   cmpt2 6298 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-opab 4516  df-id 4804  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-dm 5018  df-iota 5557  df-fun 5596  df-fv 5602  df-ov 6299  df-oprab 6300  df-mpt2 6301 This theorem is referenced by:  xpcco  15579  curf12  15623  curf2  15625
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