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Theorem ovmpt2dv2 6207
 Description: Alternate deduction version of ovmpt2 6209, 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:   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)

Proof of Theorem ovmpt2dv2
StepHypRef Expression
1 eqidd 2437 . . 3
2 ovmpt2dv2.1 . . . 4
3 ovmpt2dv2.2 . . . 4
4 ovmpt2dv2.3 . . . 4
5 ovmpt2dv2.4 . . . . . 6
65eqeq2d 2447 . . . . 5
76biimpd 199 . . . 4
8 nfmpt21 6140 . . . 4
9 nfcv 2572 . . . . . 6
10 nfcv 2572 . . . . . 6
119, 8, 10nfov 6104 . . . . 5
1211nfeq1 2581 . . . 4
13 nfmpt22 6141 . . . 4
14 nfcv 2572 . . . . . 6
15 nfcv 2572 . . . . . 6
1614, 13, 15nfov 6104 . . . . 5
1716nfeq1 2581 . . . 4
182, 3, 4, 7, 8, 12, 13, 17ovmpt2df 6205 . . 3
191, 18mpd 15 . 2
20 oveq 6087 . . 3
2120eqeq1d 2444 . 2
2219, 21syl5ibrcom 214 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  (class class class)co 6081   cmpt2 6083 This theorem is referenced by:  coaval  14223  xpcco  14280  nbgraop  21436  isuvtx  21497 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-iota 5418  df-fun 5456  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086
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