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Theorem equncomiVD 41746
Description: Inference form of equncom 4084. 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 4085 is equncomiVD 41746 without virtual deductions and was automatically derived from equncomiVD 41746.
 h1:: ⊢ 𝐴 = (𝐵 ∪ 𝐶) qed:1: ⊢ 𝐴 = (𝐶 ∪ 𝐵)
(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 4084 . . 3 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
32biimpi 219 . 2 (𝐴 = (𝐵𝐶) → 𝐴 = (𝐶𝐵))
41, 3e0a 41649 1 𝐴 = (𝐶𝐵)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∪ cun 3881 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-un 3888 This theorem is referenced by: (None)
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