Theorem equncomiVD 44841

Description: Inference form of equncom 4134. 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 4135 is equncomiVD 44841 without virtual deductions and was automatically derived from equncomiVD 44841.

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 = (𝐵 ∪ 𝐶)

Assertion

Ref	Expression
equncomiVD	⊢ 𝐴 = (𝐶 ∪ 𝐵)

Proof of Theorem equncomiVD

Step	Hyp	Ref	Expression
1		equncomiVD.1	. 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶)
2		equncom 4134	. . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	2	biimpi 216	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵))
4	1, 3	e0a 44744	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

Syntax hints:   = wceq 1540   ∪ cun 3924

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 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-v 3461  df-un 3931

This theorem is referenced by: (None)