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)

Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642  dom cdm 4773   Fn wfn 4777

This theorem was proved from 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 theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-fn 4791

This theorem is referenced by:  fodmrnu  5278