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Theorem ovmpt2dv2 6436
Description: Alternate deduction version of ovmpt2 6438, suitable for iteration. (Contributed by Mario Carneiro, 7-Jan-2017.)
Hypotheses
Ref Expression
ovmpt2dv2.1
ovmpt2dv2.2
ovmpt2dv2.3
ovmpt2dv2.4
Assertion
Ref Expression
ovmpt2dv2
Distinct variable groups:   , ,   , ,   , ,   ,S,

Proof of Theorem ovmpt2dv2
StepHypRef Expression
1 eqidd 2458 . . 3
2 ovmpt2dv2.1 . . . 4
3 ovmpt2dv2.2 . . . 4
4 ovmpt2dv2.3 . . . 4
5 ovmpt2dv2.4 . . . . . 6
65eqeq2d 2471 . . . . 5
76biimpd 207 . . . 4
8 nfmpt21 6364 . . . 4
9 nfcv 2619 . . . . . 6
10 nfcv 2619 . . . . . 6
119, 8, 10nfov 6322 . . . . 5
1211nfeq1 2634 . . . 4
13 nfmpt22 6365 . . . 4
14 nfcv 2619 . . . . . 6
15 nfcv 2619 . . . . . 6
1614, 13, 15nfov 6322 . . . . 5
1716nfeq1 2634 . . . 4
182, 3, 4, 7, 8, 12, 13, 17ovmpt2df 6434 . . 3
191, 18mpd 15 . 2
20 oveq 6302 . . 3
2120eqeq1d 2459 . 2
2219, 21syl5ibrcom 222 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  (class class class)co 6296  e.cmpt2 6298
This theorem is referenced by:  coaval  15395  xpcco  15452  marrepval  19064  marrepeval  19065  marepveval  19070  submaval  19083  submaeval  19084  minmar1val  19150  minmar1eval  19151  nbgraop  24423  isuvtx  24488
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  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 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301
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