Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  equncomiVD Structured version   Visualization version   GIF version

Theorem equncomiVD 43630
Description: Inference form of equncom 4155. The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. equncomi 4156 is equncomiVD 43630 without virtual deductions and was automatically derived from equncomiVD 43630.
h1:: 𝐴 = (𝐵𝐶)
qed:1: 𝐴 = (𝐶𝐵)
(Contributed by Alan Sare, 18-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
equncomiVD.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
equncomiVD 𝐴 = (𝐶𝐵)

Proof of Theorem equncomiVD
StepHypRef Expression
1 equncomiVD.1 . 2 𝐴 = (𝐵𝐶)
2 equncom 4155 . . 3 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
32biimpi 215 . 2 (𝐴 = (𝐵𝐶) → 𝐴 = (𝐶𝐵))
41, 3e0a 43533 1 𝐴 = (𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cun 3947
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-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3954
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator