Theorem equncomiVD 45637

Description: Inference form of equncom 4113. 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 4114 is equncomiVD 45637 without virtual deductions and was automatically derived from equncomiVD 45637.

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 4113	. . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	2	biimpi 219	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵))
4	1, 3	e0a 45540	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

This proof depends on syntax axioms:   = wceq 1570   ∪ cun 3904

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-un 3911

This theorem is used by: (None)