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Theorem f1oeq2 5061
Description: Equality theorem for one-to-one onto functions. (Contributed by NM, 10-Feb-1997.)
Assertion
Ref Expression
f1oeq2  F : -1-1-onto-> C  F : -1-1-onto-> C

Proof of Theorem f1oeq2
StepHypRef Expression
1 f1eq2 5031 . . 3  F : -1-1-> C  F : -1-1-> C
2 foeq2 5046 . . 3  F : -onto-> C  F : -onto-> C
31, 2anbi12d 442 . 2  F : -1-1-> C  F : -onto-> C  F : -1-1-> C  F : -onto-> C
4 df-f1o 4852 . 2  F : -1-1-onto-> C  F : -1-1-> C  F : -onto-> C
5 df-f1o 4852 . 2  F : -1-1-onto-> C  F : -1-1-> C  F : -onto-> C
63, 4, 53bitr4g 212 1  F : -1-1-onto-> C  F : -1-1-onto-> C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   -1-1->wf1 4842   -onto->wfo 4843   -1-1-onto->wf1o 4844
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-fn 4848  df-f 4849  df-f1 4850  df-fo 4851  df-f1o 4852
This theorem is referenced by:  f1oeq23  5063  f1oeq123d  5066  f1osng  5110  isoeq4  5387  bren  6164
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