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Theorem u2lemc1 681
 Description: Commutation theorem for Dishkant implication.
Assertion
Ref Expression
u2lemc1 b C (a2 b)

Proof of Theorem u2lemc1
StepHypRef Expression
1 comid 187 . . 3 b C b
2 comanr2 465 . . . 4 b C (ab )
32comcom6 459 . . 3 b C (ab )
41, 3com2or 483 . 2 b C (b ∪ (ab ))
5 df-i2 45 . . 3 (a2 b) = (b ∪ (ab ))
65ax-r1 35 . 2 (b ∪ (ab )) = (a2 b)
74, 6cbtr 182 1 b C (a2 b)
 Colors of variables: term Syntax hints:   C wc 3  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →2 wi2 13 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  u2lemc3  692  u21lembi  727  u2lem3  750  imp3  841  oa23  936
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