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Theorem u5lemc2 690
Description: Commutation theorem for relevance implication.
Hypotheses
Ref Expression
ulemc2.1 a C b
ulemc2.2 a C c
Assertion
Ref Expression
u5lemc2 a C (b ->5 c)
Proof of Theorem u5lemc2
StepHypRef Expression
1 ulemc2.1 . . . . 5 a C b
2 ulemc2.2 . . . . 5 a C c
31, 2com2an 484 . . . 4 a C (b ^ c)
41comcom2 183 . . . . 5 a C b'
54, 2com2an 484 . . . 4 a C (b' ^ c)
63, 5com2or 483 . . 3 a C ((b ^ c) v (b' ^ c))
72comcom2 183 . . . 4 a C c'
84, 7com2an 484 . . 3 a C (b' ^ c')
96, 8com2or 483 . 2 a C (((b ^ c) v (b' ^ c)) v (b' ^ c'))
10 df-i5 48 . . 3 (b ->5 c) = (((b ^ c) v (b' ^ c)) v (b' ^ c'))
1110ax-r1 35 . 2 (((b ^ c) v (b' ^ c)) v (b' ^ c')) = (b ->5 c)
129, 11cbtr 182 1 a C (b ->5 c)
Colors of variables: term
Syntax hints:   C wc 3  'wn 4   v 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: (None)
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