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Theorem fndmu 5184
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
StepHypRef Expression
1 fndm 5182 . 2 (F Fn A → dom F = A)
2 fndm 5182 . 2 (F Fn B → dom F = B)
31, 2sylan9req 2406 1 ((F Fn A F Fn B) → A = B)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   = wceq 1642  dom cdm 4772   Fn wfn 4776
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 4790
This theorem is referenced by:  fodmrnu  5277
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