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Theorem f1fn 5121
Description: A one-to-one mapping is a function on its domain. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1fn (𝐹:𝐴1-1𝐵𝐹 Fn 𝐴)

Proof of Theorem f1fn
StepHypRef Expression
1 f1f 5120 . 2 (𝐹:𝐴1-1𝐵𝐹:𝐴𝐵)
2 ffn 5074 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
31, 2syl 14 1 (𝐹:𝐴1-1𝐵𝐹 Fn 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   Fn wfn 4925  wf 4926  1-1wf1 4927
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103
This theorem depends on definitions:  df-bi 114  df-f 4934  df-f1 4935
This theorem is referenced by:  f1fun  5122  f1rel  5123  f1dm  5124  f1ssr  5126  f1f1orn  5165  f1elima  5440  f1eqcocnv  5459  f1oiso  5493  phplem4dom  6355
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