Theorem fndmu 5336

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 5334	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5334	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2243	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 104   = wceq 1364   dom cdm 4644   Fn wfn 5230

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 1458  ax-gen 1460  ax-4 1521  ax-17 1537  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-cleq 2182  df-fn 5238

This theorem is referenced by:  fodmrnu  5465  tfrlemisucaccv  6349  tfr1onlemsucaccv  6365  tfrcllemsucaccv  6378  0fz1  10074  lmodfopnelem1  13637