Theorem fndmu 5992

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 5990	. 2 |- ( F Fn A -> dom F = A )
2		fndm 5990	. 2 |- ( F Fn B -> dom F = B )
3	1, 2	sylan9req 2677	1 |- ( ( F Fn A /\ F Fn B ) -> A = B )

Syntax hints:   -> wi 4   /\ wa 384   = wceq 1483   dom cdm 5114   Fn wfn 5883

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615  df-fn 5891

This theorem is referenced by:  fodmrnu  6123  0fz1  12361  lmodfopnelem1  18899  grporn  27375  hon0  28652  2ffzoeq  41338