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Theorem equncomiVD 39604
Description: Inference form of equncom 3901. 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 3902 is equncomiVD 39604 without virtual deductions and was automatically derived from equncomiVD 39604.
 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 3901 . . 3 (𝐴 = (𝐵𝐶) ↔ 𝐴 = (𝐶𝐵))
32biimpi 206 . 2 (𝐴 = (𝐵𝐶) → 𝐴 = (𝐶𝐵))
41, 3e0a 39501 1 𝐴 = (𝐶𝐵)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1632   ∪ cun 3713 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-un 3720 This theorem is referenced by: (None)
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