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Theorem equncomiVD 32966
Description: Inference form of equncom 3649. 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 3650 is equncomiVD 32966 without virtual deductions and was automatically derived from equncomiVD 32966.
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
StepHypRef Expression
1 equncomiVD.1 . 2  |-  A  =  ( B  u.  C
)
2 equncom 3649 . . 3  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
32biimpi 194 . 2  |-  ( A  =  ( B  u.  C )  ->  A  =  ( C  u.  B ) )
41, 3e0a 32866 1  |-  A  =  ( C  u.  B
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    u. cun 3474
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-un 3481
This theorem is referenced by: (None)
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