Theorem fndmu 3589

Description: A function has a unique domain.

Assertion

Ref	Expression
fndmu	|- ((F Fn A /\ F Fn B) -> A = B)

Proof of Theorem fndmu

Step	Hyp	Ref	Expression
1		fndm 3587	. 2 |- (F Fn A -> dom F = A)
2		fndm 3587	. 2 |- (F Fn B -> dom F = B)
3	1, 2	sylan9req 1528	1 |- ((F Fn A /\ F Fn B) -> A = B)

Syntax hints:   -> wi 3   /\ wa 223   = wceq 956  dom cdm 3170   Fn wfn 3177

This theorem is referenced by:  fodmrnu 3680  grprn 8056  vcoprnelem 8197  hon0 9719

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-17 971  ax-4 973  ax-5o 975  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1469  df-fn 3193

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