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Theorem equncomi 3410
 Description: Inference form of equncom 3409. equncomi 3410 was automatically derived from equncomiVD in set.mm using the tools program translate_without_overwriting.cmd and minimizing. (Contributed by Alan Sare, 18-Feb-2012.)
Hypothesis
Ref Expression
equncomi.1 A = (BC)
Assertion
Ref Expression
equncomi A = (CB)

Proof of Theorem equncomi
StepHypRef Expression
1 equncomi.1 . 2 A = (BC)
2 equncom 3409 . 2 (A = (BC) ↔ A = (CB))
31, 2mpbi 199 1 A = (CB)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∪ cun 3207 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214 This theorem is referenced by:  disjssun  3608  difprsn1  3847
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