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Theorem equncomiVD 44866
Description: Inference form of equncom 4168. 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 4169 is equncomiVD 44866 without virtual deductions and was automatically derived from equncomiVD 44866.
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 4168 . . 3 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
32biimpi 216 . 2 (𝐴 = (𝐵𝐶) → 𝐴 = (𝐶𝐵))
41, 3e0a 44769 1 𝐴 = (𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1536  cun 3960
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-un 3967
This theorem is referenced by: (None)
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