Theorem fndmu 5289

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 5287	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5287	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2220	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 103   = wceq 1343   dom cdm 4604   Fn wfn 5183

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 1435  ax-gen 1437  ax-4 1498  ax-17 1514  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-cleq 2158  df-fn 5191

This theorem is referenced by:  fodmrnu  5418  tfrlemisucaccv  6293  tfr1onlemsucaccv  6309  tfrcllemsucaccv  6322  0fz1  9980