MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  fndmu Structured version   Visualization version   GIF version

Theorem fndmu 5980
Description: A function has a unique domain. (Contributed by NM, 11-Aug-1994.)
Assertion
Ref Expression
fndmu ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)

Proof of Theorem fndmu
StepHypRef Expression
1 fndm 5978 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 5978 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2675 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384   = wceq 1481  dom cdm 5104   Fn wfn 5871
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1703  df-cleq 2613  df-fn 5879
This theorem is referenced by:  fodmrnu  6110  0fz1  12346  lmodfopnelem1  18880  grporn  27345  hon0  28622  2ffzoeq  41101
  Copyright terms: Public domain W3C validator