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Theorem f1of1 5153
Description: A one-to-one onto mapping is a one-to-one mapping. (Contributed by NM, 12-Dec-2003.)
Assertion
Ref Expression
f1of1 (𝐹:𝐴1-1-onto𝐵𝐹:𝐴1-1𝐵)

Proof of Theorem f1of1
StepHypRef Expression
1 df-f1o 4937 . 2 (𝐹:𝐴1-1-onto𝐵 ↔ (𝐹:𝐴1-1𝐵𝐹:𝐴onto𝐵))
21simplbi 263 1 (𝐹:𝐴1-1-onto𝐵𝐹:𝐴1-1𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  1-1wf1 4927  ontowfo 4928  1-1-ontowf1o 4929
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-f1o 4937
This theorem is referenced by:  f1of  5154  f1oresrab  5357  f1ocnvfvrneq  5450  isores3  5483  isoini2  5486  f1oiso  5493  f1opw2  5734  tposf12  5915  enssdom  6273  phplem4  6349  phplem4on  6360  fidceq  6361  isotilem  6410
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