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Theorem f1dm 5124
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 5121 . 2 (𝐹:𝐴1-1𝐵𝐹 Fn 𝐴)
2 fndm 5026 . 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 1259  dom cdm 4373   Fn wfn 4925  1-1wf1 4927
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 4933  df-f 4934  df-f1 4935
This theorem is referenced by:  fun11iun  5175  tposf12  5915
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