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Theorem equncomiVD 44889
Description: Inference form of equncom 4159. 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 4160 is equncomiVD 44889 without virtual deductions and was automatically derived from equncomiVD 44889.
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 4159 . . 3 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
32biimpi 216 . 2 (𝐴 = (𝐵𝐶) → 𝐴 = (𝐶𝐵))
41, 3e0a 44792 1 𝐴 = (𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cun 3949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956
This theorem is referenced by: (None)
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