Users' Mathboxes Mathbox for Thierry Arnoux < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  feq3dd Structured version   Visualization version   GIF version

Theorem feq3dd 32490
Description: Equality deduction for functions. (Contributed by Thierry Arnoux, 27-May-2025.)
Hypotheses
Ref Expression
feq3dd.eq (𝜑𝐵 = 𝐶)
feq3dd.f (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
feq3dd (𝜑𝐹:𝐴𝐶)

Proof of Theorem feq3dd
StepHypRef Expression
1 feq3dd.f . 2 (𝜑𝐹:𝐴𝐵)
2 feq3dd.eq . . 3 (𝜑𝐵 = 𝐶)
32feq3d 6710 . 2 (𝜑 → (𝐹:𝐴𝐵𝐹:𝐴𝐶))
41, 3mpbid 231 1 (𝜑𝐹:𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wf 6545
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1774  df-cleq 2717  df-ss 3961  df-f 6553
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator