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Theorem equncomiVD 28961
Description: Inference form of equncom 3333. 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 3334 is equncomiVD 28961 without virtual deductions and was automatically derived from equncomiVD 28961.
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 3333 . . 3  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
32biimpi 186 . 2  |-  ( A  =  ( B  u.  C )  ->  A  =  ( C  u.  B ) )
41, 3e0_ 28861 1  |-  A  =  ( C  u.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1632    u. cun 3163
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170
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