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Theorem fndmu 4943
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
StepHypRef Expression
1 fndm 4941 . 2 (𝐹 Fn A → dom 𝐹 = A)
2 fndm 4941 . 2 (𝐹 Fn B → dom 𝐹 = B)
31, 2sylan9req 2090 1 ((𝐹 Fn A 𝐹 Fn B) → A = B)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   = wceq 1242  dom cdm 4288   Fn wfn 4840
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-fn 4848
This theorem is referenced by:  fodmrnu  5057  tfrlemisucaccv  5880  0fz1  8679
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