Theorem fndmu 5359

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 5357	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5357	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2250	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 104   = wceq 1364   dom cdm 4663   Fn wfn 5253

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 1461  ax-gen 1463  ax-4 1524  ax-17 1540  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-fn 5261

This theorem is referenced by:  fodmrnu  5488  tfrlemisucaccv  6383  tfr1onlemsucaccv  6399  tfrcllemsucaccv  6412  0fz1  10120  lmodfopnelem1  13880