Theorem fndmu 5378

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 5374	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5374	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2259	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 104   = wceq 1373   dom cdm 4676   Fn wfn 5267

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 1470  ax-gen 1472  ax-4 1533  ax-17 1549  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-cleq 2198  df-fn 5275

This theorem is referenced by:  fodmrnu  5508  tfrlemisucaccv  6413  tfr1onlemsucaccv  6429  tfrcllemsucaccv  6442  0fz1  10169  lmodfopnelem1  14119