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Theorem ovidig 6319
 Description: The value of an operation class abstraction. Compare ovidi 6320. 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 6204 . 2
2 ovidig.1 . . . . 5
32funoprab 6301 . . . 4
4 ovidig.2 . . . . 5
54funeqi 5547 . . . 4
63, 5mpbir 209 . . 3
7 oprabid 6225 . . . . 5
87biimpri 206 . . . 4
98, 4syl6eleqr 2553 . . 3
10 funopfv 5841 . . 3
116, 9, 10mpsyl 63 . 2
121, 11syl5eq 2507 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1370   wcel 1758  wmo 2263  cop 3992   wfun 5521  cfv 5527  (class class class)co 6201  coprab 6202 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4522  ax-nul 4530  ax-pr 4640 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-sbc 3295  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-sn 3987  df-pr 3989  df-op 3993  df-uni 4201  df-br 4402  df-opab 4460  df-id 4745  df-xp 4955  df-rel 4956  df-cnv 4957  df-co 4958  df-dm 4959  df-iota 5490  df-fun 5529  df-fv 5535  df-ov 6204  df-oprab 6205 This theorem is referenced by:  ovidi  6320
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