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Theorem f1eq123d 5661
 Description: Equality deduction for one-to-one functions. (Contributed by Mario Carneiro, 27-Jan-2017.)
Hypotheses
Ref Expression
f1eq123d.1
f1eq123d.2
f1eq123d.3
Assertion
Ref Expression
f1eq123d

Proof of Theorem f1eq123d
StepHypRef Expression
1 f1eq123d.1 . . 3
2 f1eq1 5626 . . 3
31, 2syl 16 . 2
4 f1eq123d.2 . . 3
5 f1eq2 5627 . . 3
64, 5syl 16 . 2
7 f1eq123d.3 . . 3
8 f1eq3 5628 . . 3
97, 8syl 16 . 2
103, 6, 93bitrd 271 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652  wf1 5443 This theorem is referenced by:  fthf1  14106  cofth  14124  usgraeq12d  21377  usgra0v  21383  usgra1v  21401  usgrares1  21416  usgra2pthspth  28248  2spontn0vne  28297 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  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-br 4205  df-opab 4259  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451
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