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Theorem u5lemc1 684
 Description: Commutation theorem for relevance implication.
Assertion
Ref Expression
u5lemc1 a C (a5 b)

Proof of Theorem u5lemc1
StepHypRef Expression
1 comanr1 464 . . . 4 a C (ab)
2 comanr1 464 . . . . 5 a C (ab)
32comcom6 459 . . . 4 a C (ab)
41, 3com2or 483 . . 3 a C ((ab) ∪ (ab))
5 comanr1 464 . . . 4 a C (ab )
65comcom6 459 . . 3 a C (ab )
74, 6com2or 483 . 2 a C (((ab) ∪ (ab)) ∪ (ab ))
8 df-i5 48 . . 3 (a5 b) = (((ab) ∪ (ab)) ∪ (ab ))
98ax-r1 35 . 2 (((ab) ∪ (ab)) ∪ (ab )) = (a5 b)
107, 9cbtr 182 1 a C (a5 b)
 Colors of variables: term Syntax hints:   C wc 3  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →5 wi5 16 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-i5 48  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  u5lemc5  700  u5lembi  725  u5lem1  738  u5lem4  760  u5lem5  765  u5lem6  769
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