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Theorem u1lemc2 686
Description: Commutation theorem for Sasaki implication.
Hypotheses
Ref Expression
ulemc2.1 a C b
ulemc2.2 a C c
Assertion
Ref Expression
u1lemc2 a C (b ->1 c)
Proof of Theorem u1lemc2
StepHypRef Expression
1 ulemc2.1 . . . 4 a C b
21comcom2 183 . . 3 a C b'
3 ulemc2.2 . . . 4 a C c
41, 3com2an 484 . . 3 a C (b ^ c)
52, 4com2or 483 . 2 a C (b' v (b ^ c))
6 df-i1 44 . . 3 (b ->1 c) = (b' v (b ^ c))
76ax-r1 35 . 2 (b' v (b ^ c)) = (b ->1 c)
85, 7cbtr 182 1 a C (b ->1 c)
Colors of variables: term
Syntax hints:   C wc 3  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
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-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  u1lemc3  691
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