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Theorem equncomiVD 28982
Description: Inference form of equncom 3493. The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. equncomi 3494 is equncomiVD 28982 without virtual deductions and was automatically derived from equncomiVD 28982.
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 3493 . . 3  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
32biimpi 188 . 2  |-  ( A  =  ( B  u.  C )  ->  A  =  ( C  u.  B ) )
41, 3e0_ 28885 1  |-  A  =  ( C  u.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1653    u. cun 3319
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-un 3326
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