Theorem fndmu 5458

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 5454	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5454	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2286	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 104   = wceq 1398   dom cdm 4748   Fn wfn 5346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-gen 1498  ax-4 1559  ax-17 1575  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-cleq 2225  df-fn 5354

This theorem is referenced by:  fodmrnu  5597  tfrlemisucaccv  6555  tfr1onlemsucaccv  6571  tfrcllemsucaccv  6584  0fz1  10375  lmodfopnelem1  14459