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Theorem equncomi 3650
Description: Inference form of equncom 3649. equncomi 3650 was automatically derived from equncomiVD 32749 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 3649 . 2  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
31, 2mpbi 208 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:  disjssun  3884  difprsn1  4163  unidmrn  5535  phplem1  7693  ackbij1lem14  8609  ltxrlt  9651  ruclem6  13825  ruclem7  13826  i1f1  21832  subfacp1lem1  28263  pwfi2f1o  30648  usgfislem1  31913  usgfisALTlem1  31917  sucidALTVD  32750  sucidALT  32751
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