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Theorem foeq123d 5827
 Description: Equality deduction for onto functions. (Contributed by Mario Carneiro, 27-Jan-2017.)
Hypotheses
Ref Expression
f1eq123d.1
f1eq123d.2
f1eq123d.3
Assertion
Ref Expression
foeq123d

Proof of Theorem foeq123d
StepHypRef Expression
1 f1eq123d.1 . . 3
2 foeq1 5806 . . 3
31, 2syl 17 . 2
4 f1eq123d.2 . . 3
5 foeq2 5807 . . 3
64, 5syl 17 . 2
7 f1eq123d.3 . . 3
8 foeq3 5808 . . 3
97, 8syl 17 . 2
103, 6, 93bitrd 282 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wceq 1437  wfo 5599 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-br 4427  df-opab 4485  df-rel 4861  df-cnv 4862  df-co 4863  df-dm 4864  df-rn 4865  df-fun 5603  df-fn 5604  df-fo 5607 This theorem is referenced by:  fullfo  15768  cofull  15790  efabl  23364
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