Theorem fndmu 5484

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 5480	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5480	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2292	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   = wceq 1402   dom cdm 4774   Fn wfn 5372

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-4 1563  ax-17 1579  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-fn 5380

This theorem is used by:  fodmrnu  5623  tfrlemisucaccv  6596  tfr1onlemsucaccv  6612  tfrcllemsucaccv  6625  0fz1  10449  lmodfopnelem1  14661