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Theorem ovmpt2df 6434
 Description: Alternate deduction version of ovmpt2 6438, suitable for iteration. (Contributed by Mario Carneiro, 7-Jan-2017.)
Hypotheses
Ref Expression
ovmpt2df.1
ovmpt2df.2
ovmpt2df.3
ovmpt2df.4
ovmpt2df.5
ovmpt2df.6
ovmpt2df.7
ovmpt2df.8
Assertion
Ref Expression
ovmpt2df
Distinct variable groups:   ,,   ,   ,,

Proof of Theorem ovmpt2df
StepHypRef Expression
1 nfv 1707 . 2
2 ovmpt2df.5 . . . 4
3 nfmpt21 6364 . . . 4
42, 3nfeq 2630 . . 3
5 ovmpt2df.6 . . 3
64, 5nfim 1920 . 2
7 ovmpt2df.1 . . . 4
8 elex 3118 . . . 4
97, 8syl 16 . . 3
10 isset 3113 . . 3
119, 10sylib 196 . 2
12 ovmpt2df.2 . . . . 5
13 elex 3118 . . . . 5
1412, 13syl 16 . . . 4
15 isset 3113 . . . 4
1614, 15sylib 196 . . 3
17 nfv 1707 . . . 4
18 ovmpt2df.7 . . . . . 6
19 nfmpt22 6365 . . . . . 6
2018, 19nfeq 2630 . . . . 5
21 ovmpt2df.8 . . . . 5
2220, 21nfim 1920 . . . 4
23 oveq 6302 . . . . . 6
24 simprl 756 . . . . . . . . . 10
25 simprr 757 . . . . . . . . . 10
2624, 25oveq12d 6314 . . . . . . . . 9
277adantr 465 . . . . . . . . . . 11
2824, 27eqeltrd 2545 . . . . . . . . . 10
2912adantrr 716 . . . . . . . . . . 11
3025, 29eqeltrd 2545 . . . . . . . . . 10
31 ovmpt2df.3 . . . . . . . . . 10
32 eqid 2457 . . . . . . . . . . 11
3332ovmpt4g 6425 . . . . . . . . . 10
3428, 30, 31, 33syl3anc 1228 . . . . . . . . 9
3526, 34eqtr3d 2500 . . . . . . . 8
3635eqeq2d 2471 . . . . . . 7
37 ovmpt2df.4 . . . . . . 7
3836, 37sylbid 215 . . . . . 6
3923, 38syl5 32 . . . . 5
4039expr 615 . . . 4
4117, 22, 40exlimd 1914 . . 3
4216, 41mpd 15 . 2
431, 6, 11, 42exlimdd 1980 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818  F/_wnfc 2605   cvv 3109  (class class class)co 6296  e.cmpt2 6298 This theorem is referenced by:  ovmpt2dv  6435  ovmpt2dv2  6436 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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