Theorem equncomiVD 39105

Description: Inference form of equncom 3758. 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 3759 is equncomiVD 39105 without virtual deductions and was automatically derived from equncomiVD 39105.

h1::	|- A = ( B u. C )
qed:1:	|- A = ( C u. B )

(Contributed by Alan Sare, 18-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
equncomiVD.1	|- A = ( B u. C )

Assertion

Ref	Expression
equncomiVD	|- A = ( C u. B )

Proof of Theorem equncomiVD

Step	Hyp	Ref	Expression
1		equncomiVD.1	. 2 |- A = ( B u. C )
2		equncom 3758	. . 3 |- ( A = ( B u. C ) <-> A = ( C u. B ) )
3	2	biimpi 206	. 2 |- ( A = ( B u. C ) -> A = ( C u. B ) )
4	1, 3	e0a 38999	1 |- A = ( C u. B )

Syntax hints:   = wceq 1483   u. cun 3572

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579

This theorem is referenced by: (None)