Theorem equncomiVD 44842

Description: Inference form of equncom 4110. 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 4111 is equncomiVD 44842 without virtual deductions and was automatically derived from equncomiVD 44842.

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 4110	. . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	2	biimpi 216	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵))
4	1, 3	e0a 44745	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

Syntax hints:   = wceq 1540   ∪ cun 3901

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 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3438  df-un 3908

This theorem is referenced by: (None)