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Theorem f1odm 5155
Description: The domain of a one-to-one onto mapping. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1odm (𝐹:𝐴1-1-onto𝐵 → dom 𝐹 = 𝐴)

Proof of Theorem f1odm
StepHypRef Expression
1 f1ofn 5152 . 2 (𝐹:𝐴1-1-onto𝐵𝐹 Fn 𝐴)
2 fndm 5023 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
31, 2syl 14 1 (𝐹:𝐴1-1-onto𝐵 → dom 𝐹 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1257  dom cdm 4370   Fn wfn 4922  1-1-ontowf1o 4926
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104
This theorem depends on definitions:  df-bi 114  df-fn 4930  df-f 4931  df-f1 4932  df-f1o 4934
This theorem is referenced by:  f1imacnv  5168  f1opw2  5731  xpcomco  6328  phplem4  6346  phplem4on  6357  dif1en  6365
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