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Theorem opabiotafun 6528
 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 5478 . . 3
2 mo2icl 3105 . . . . 5
3 unieq 4016 . . . . . 6
4 vex 2951 . . . . . . 7
54unisn 4023 . . . . . 6
63, 5syl6req 2484 . . . . 5
72, 6mpg 1557 . . . 4
8 nfv 1629 . . . . 5
9 nfab1 2573 . . . . . 6
109nfeq1 2580 . . . . 5
11 sneq 3817 . . . . . 6
1211eqeq2d 2446 . . . . 5
138, 10, 12cbvmo 2317 . . . 4
147, 13mpbir 201 . . 3
151, 14mpgbir 1559 . 2
16 opabiota.1 . . 3
1716funeqi 5466 . 2
1815, 17mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652  wmo 2281  cab 2421  csn 3806  cuni 4007  copab 4257   wfun 5440 This theorem is referenced by:  opabiota  6530 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-fun 5448
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