Theorem f1dm 5583

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

Assertion

Ref	Expression
f1dm	|- ( F : A -1-1-> B -> dom F = A )

Proof of Theorem f1dm

Step	Hyp	Ref	Expression
1		f1fn 5580	. 2 |- ( F : A -1-1-> B -> F Fn A )
2		fndm 5460	. 2 |- ( F Fn A -> dom F = A )
3	1, 2	syl 14	1 |- ( F : A -1-1-> B -> dom F = A )

Syntax hints:   -> wi 4   = wceq 1398   dom cdm 4754   Fn wfn 5352   -1-1->wf1 5354

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem depends on definitions:  df-bi 117  df-fn 5360  df-f 5361  df-f1 5362

This theorem is referenced by:  fun11iun  5640  tposf12  6513  f1dmvrnfibi  7224  f1vrnfibi  7225  exmidfodomrlemim  7517  hmeoimaf1o  15308  uspgr1edc  16364  exmidsbthrlem  16941