Theorem f1odm 5150

Description: The domain of a one-to-one onto mapping. (Contributed by NM, 8-Mar-2014.)

Assertion

Ref	Expression
f1odm	|- ( F : A -1-1-onto-> B -> dom F = A )

Proof of Theorem f1odm

Step	Hyp	Ref	Expression
1		f1ofn 5147	. 2 |- ( F : A -1-1-onto-> B -> F Fn A )
2		fndm 5018	. 2 |- ( F Fn A -> dom F = A )
3	1, 2	syl 14	1 |- ( F : A -1-1-onto-> B -> dom F = A )

Syntax hints:   -> wi 4   = wceq 1284   dom cdm 4363   Fn wfn 4917   -1-1-onto->wf1o 4921

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105

This theorem depends on definitions:  df-bi 115  df-fn 4925  df-f 4926  df-f1 4927  df-f1o 4929

This theorem is referenced by:  f1imacnv  5163  f1opw2  5726  xpcomco  6323  phplem4  6341  phplem4on  6353  dif1en  6364