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Theorem equncomi 3321
Description: Inference form of equncom 3320. equncomi 3321 was automatically derived from equncomiVD 28645 using the tools program translatewithout_overwriting.cmd and minimizing. (Contributed by Alan Sare, 18-Feb-2012.)
Hypothesis
Ref Expression
equncomi.1  |-  A  =  ( B  u.  C
)
Assertion
Ref Expression
equncomi  |-  A  =  ( C  u.  B
)

Proof of Theorem equncomi
StepHypRef Expression
1 equncomi.1 . 2  |-  A  =  ( B  u.  C
)
2 equncom 3320 . 2  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
31, 2mpbi 199 1  |-  A  =  ( C  u.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    u. cun 3150
This theorem is referenced by:  disjssun  3512  unidmrn  5202  ackbij1lem14  7859  ltxrlt  8893  ruclem6  12513  ruclem7  12514  subfacp1lem1  23710  pwfi2f1o  27260  sucidALTVD  28646  sucidALT  28647
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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