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Theorem equncomi 3495
Description: Inference form of equncom 3494. equncomi 3495 was automatically derived from equncomiVD 29055 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 3494 . 2  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
31, 2mpbi 201 1  |-  A  =  ( C  u.  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1653    u. cun 3320
This theorem is referenced by:  disjssun  3687  difprsn1  3937  unidmrn  5402  phplem1  7289  ackbij1lem14  8118  ltxrlt  9151  ruclem6  12839  ruclem7  12840  i1f1  19585  subfacp1lem1  24870  pwfi2f1o  27251  sucidALTVD  29056  sucidALT  29057
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327
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