Theorem fndmu 5020

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 5018	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5018	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2134	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 102   = wceq 1284   dom cdm 4363   Fn wfn 4917

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-4 1440  ax-17 1459  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-fn 4925

This theorem is referenced by:  fodmrnu  5134  tfrlemisucaccv  5962  0fz1  9064