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Theorem f1dm 5039
Description: The domain of a one-to-one mapping. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1dm (𝐹:A1-1B → dom 𝐹 = A)

Proof of Theorem f1dm
StepHypRef Expression
1 f1fn 5036 . 2 (𝐹:A1-1B𝐹 Fn A)
2 fndm 4941 . 2 (𝐹 Fn A → dom 𝐹 = A)
31, 2syl 14 1 (𝐹:A1-1B → dom 𝐹 = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  dom cdm 4288   Fn wfn 4840  1-1wf1 4842
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110  df-fn 4848  df-f 4849  df-f1 4850
This theorem is referenced by:  fun11iun  5090  tposf12  5825
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