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Theorem ovidig 6191
 Description: The value of an operation class abstraction. Compare ovidi 6192. The condition is been removed. (Contributed by Mario Carneiro, 29-Dec-2014.)
Hypotheses
Ref Expression
ovidig.1
ovidig.2
Assertion
Ref Expression
ovidig
Distinct variable group:   ,,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem ovidig
StepHypRef Expression
1 df-ov 6084 . 2
2 ovidig.1 . . . . 5
32funoprab 6170 . . . 4
4 ovidig.2 . . . . 5
54funeqi 5474 . . . 4
63, 5mpbir 201 . . 3
7 oprabid 6105 . . . . 5
87biimpri 198 . . . 4
98, 4syl6eleqr 2527 . . 3
10 funopfv 5766 . . 3
116, 9, 10mpsyl 61 . 2
121, 11syl5eq 2480 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wmo 2282  cop 3817   wfun 5448  cfv 5454  (class class class)co 6081  coprab 6082 This theorem is referenced by:  ovidi  6192 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
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