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Theorem equncomi 3397
Description: Inference form of equncom 3396. equncomi 3397 was automatically derived from equncomiVD 28390 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 3396 . 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 1642    u. cun 3226
This theorem is referenced by:  disjssun  3588  difprsn1  3833  unidmrn  5281  ackbij1lem14  7946  ltxrlt  8980  ruclem6  12604  ruclem7  12605  subfacp1lem1  24114  pwfi2f1o  26583  sucidALTVD  28391  sucidALT  28392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-v 2866  df-un 3233
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