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Metamath Proof Explorer

Theorem f1odm

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

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

Proof

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