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Theorem f1fn 5337
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 5335 . 2 (𝐹:𝐴1-1𝐵𝐹:𝐴𝐵)
2 ffn 5279 . 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 5125  wf 5126  1-1wf1 5127
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-f 5134  df-f1 5135
This theorem is referenced by:  f1fun  5338  f1rel  5339  f1dm  5340  f1ssr  5342  f1f1orn  5385  f1elima  5681  f1eqcocnv  5699  f1oiso  5734  phplem4dom  6763  f1finf1o  6842  updjudhcoinlf  6972  updjudhcoinrg  6973  updjud  6974  fihashf1rn  10566
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