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

Theorem fndmu 6605
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 6601 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 6601 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2799 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397   = wceq 1542  dom cdm 5631   Fn wfn 6487
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2117  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-cleq 2730  df-fn 6495
This theorem is referenced by:  fodmrnu  6760  0fz1  13391  lmodfopnelem1  20287  grporn  29268  hon0  30540  2ffzoeq  45351
  Copyright terms: Public domain W3C validator