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Theorem equncomiVD 28645
Description: Inference form of equncom 3320. 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 3321 is equncomiVD 28645 without virtual deductions and was automatically derived from equncomiVD 28645.
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 3320 . . 3  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
32biimpi 186 . 2  |-  ( A  =  ( B  u.  C )  ->  A  =  ( C  u.  B ) )
41, 3e0_ 28547 1  |-  A  =  ( C  u.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    u. cun 3150
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157
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