Theorem fndmu 5299

Description: A function has a unique domain. (Contributed by NM, 11-Aug-1994.)

Assertion

Ref	Expression
fndmu	|- ( ( F Fn A /\ F Fn B ) -> A = B )

Proof of Theorem fndmu

Step	Hyp	Ref	Expression
1		fndm 5297	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5297	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2224	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 103   = wceq 1348   dom cdm 4611   Fn wfn 5193

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-4 1503  ax-17 1519  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-cleq 2163  df-fn 5201

This theorem is referenced by:  fodmrnu  5428  tfrlemisucaccv  6304  tfr1onlemsucaccv  6320  tfrcllemsucaccv  6333  0fz1  10001