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Theorem u4lemc1 683
 Description: Commutation theorem for non-tollens implication. (Contributed by NM, 14-Dec-1997.)
Assertion
Ref Expression
u4lemc1 b C (a4 b)

Proof of Theorem u4lemc1
StepHypRef Expression
1 comanr2 465 . . . 4 b C (ab)
2 comanr2 465 . . . 4 b C (ab)
31, 2com2or 483 . . 3 b C ((ab) ∪ (ab))
4 comorr2 463 . . . 4 b C (ab)
5 comid 187 . . . . 5 b C b
65comcom2 183 . . . 4 b C b
74, 6com2an 484 . . 3 b C ((ab) ∩ b )
83, 7com2or 483 . 2 b C (((ab) ∪ (ab)) ∪ ((ab) ∩ b ))
9 df-i4 47 . . 3 (a4 b) = (((ab) ∪ (ab)) ∪ ((ab) ∩ b ))
109ax-r1 35 . 2 (((ab) ∪ (ab)) ∪ ((ab) ∩ b )) = (a4 b)
118, 10cbtr 182 1 b C (a4 b)
 Colors of variables: term Syntax hints:   C wc 3  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →4 wi4 15 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-i4 47  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  u4lemc3  694  u4lem2  747  u4lem3  752  u24lem  770
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