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Theorem opabiotafun 5934
 Description: Define a function whose value is "the unique such that ". (Contributed by NM, 19-May-2015.)
Hypothesis
Ref Expression
opabiota.1
Assertion
Ref Expression
opabiotafun
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem opabiotafun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funopab 5627 . . 3
2 mo2icl 3278 . . . . 5
3 unieq 4259 . . . . . 6
4 vex 3112 . . . . . . 7
54unisn 4266 . . . . . 6
63, 5syl6req 2515 . . . . 5
72, 6mpg 1621 . . . 4
8 nfv 1708 . . . . 5
9 nfab1 2621 . . . . . 6
109nfeq1 2634 . . . . 5
11 sneq 4042 . . . . . 6
1211eqeq2d 2471 . . . . 5
138, 10, 12cbvmo 2323 . . . 4
147, 13mpbir 209 . . 3
151, 14mpgbir 1623 . 2
16 opabiota.1 . . 3
1716funeqi 5614 . 2
1815, 17mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1395  wmo 2284  cab 2442  csn 4032  cuni 4251  copab 4514   wfun 5588 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  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-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-opab 4516  df-id 4804  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-fun 5596 This theorem is referenced by:  opabiota  5936
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