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

Proof of Theorem opabiotafun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funopab 5626 . . 3
2 mo2icl 3278 . . . . 5
3 unieq 4257 . . . . . 6
4 vex 3112 . . . . . . 7
54unisn 4264 . . . . . 6
63, 5syl6req 2515 . . . . 5
72, 6mpg 1620 . . . 4
8 nfv 1707 . . . . 5
9 nfab1 2621 . . . . . 6
109nfeq1 2634 . . . . 5
11 sneq 4039 . . . . . 6
1211eqeq2d 2471 . . . . 5
138, 10, 12cbvmo 2322 . . . 4
147, 13mpbir 209 . . 3
151, 14mpgbir 1622 . 2
16 opabiota.1 . . 3
1716funeqi 5613 . 2
1815, 17mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  E*wmo 2283  {cab 2442  {csn 4029  U.cuni 4249  {copab 4509  Funwfun 5587 This theorem is referenced by:  opabiota  5936 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-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-fun 5595
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