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Theorem ovmpt2x 6431
 Description: The value of an operation class abstraction. Variant of ovmpt2ga 6432 which does not require and to be distinct. (Contributed by Jeff Madsen, 10-Jun-2010.) (Revised by Mario Carneiro, 20-Dec-2013.)
Hypotheses
Ref Expression
ovmpt2x.1
ovmpt2x.2
ovmpt2x.3
Assertion
Ref Expression
ovmpt2x
Distinct variable groups:   ,,   ,,   ,,   ,,   ,S,

Proof of Theorem ovmpt2x
StepHypRef Expression
1 elex 3118 . 2
2 ovmpt2x.3 . . . 4
32a1i 11 . . 3
4 ovmpt2x.1 . . . 4
6 ovmpt2x.2 . . . 4
8 simp1 996 . . 3
9 simp2 997 . . 3
10 simp3 998 . . 3
113, 5, 7, 8, 9, 10ovmpt2dx 6429 . 2
121, 11syl3an3 1263 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818   cvv 3109  (class class class)co 6296  e.cmpt2 6298 This theorem is referenced by:  evls1fval  18356  ptbasfi  20082  tglngval  23938  igenval  30458  lcoop  33012 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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