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Theorem u1lemc1 680
Description: Commutation theorem for Sasaki implication.
Assertion
Ref Expression
u1lemc1 a C (a ->1 b)
Proof of Theorem u1lemc1
StepHypRef Expression
1 comid 187 . . . 4 a C a
21comcom2 183 . . 3 a C a'
3 comanr1 464 . . 3 a C (a ^ b)
42, 3com2or 483 . 2 a C (a' v (a ^ b))
5 df-i1 44 . . 3 (a ->1 b) = (a' v (a ^ b))
65ax-r1 35 . 2 (a' v (a ^ b)) = (a ->1 b)
74, 6cbtr 182 1 a C (a ->1 b)
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:  u1lemc5  696  u12lembi  726  u1lem1  734  u1lem4  757  oas  925  oau  929
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