Theorem fndmu 5185

Description: A function has a unique domain. (Contributed by set.mm contributors, 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 5183	. 2 |- (F Fn A -> dom F = A)
2		fndm 5183	. 2 |- (F Fn B -> dom F = B)
3	1, 2	sylan9req 2406	1 |- ((F Fn A /\ F Fn B) -> A = B)

This proof depends on syntax axioms:   -> wi 4   /\ wa 358   = wceq 1642  dom cdm 4773   Fn wfn 4777

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This proof depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-fn 4791

This theorem is used by:  fodmrnu  5278