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Theorem i3or 497
Description: Kalmbach implication OR builder.
Assertion
Ref Expression
i3or ((a == b)' v ((a v c) ->3 (b v c))) = 1
Proof of Theorem i3or
StepHypRef Expression
1 le1 146 . 2 ((a == b)' v ((a v c) ->3 (b v c))) =< 1
2 ka4ot 435 . . . 4 ((a == b)' v ((a v c) == (b v c))) = 1
32ax-r1 35 . . 3 1 = ((a == b)' v ((a v c) == (b v c)))
4 i3bi 496 . . . . . 6 (((a v c) ->3 (b v c)) ^ ((b v c) ->3 (a v c))) = ((a v c) == (b v c))
54ax-r1 35 . . . . 5 ((a v c) == (b v c)) = (((a v c) ->3 (b v c)) ^ ((b v c) ->3 (a v c)))
6 lea 160 . . . . 5 (((a v c) ->3 (b v c)) ^ ((b v c) ->3 (a v c))) =< ((a v c) ->3 (b v c))
75, 6bltr 138 . . . 4 ((a v c) == (b v c)) =< ((a v c) ->3 (b v c))
87lelor 166 . . 3 ((a == b)' v ((a v c) == (b v c))) =< ((a == b)' v ((a v c) ->3 (b v c)))
93, 8bltr 138 . 2 1 =< ((a == b)' v ((a v c) ->3 (b v c)))
101, 9lebi 145 1 ((a == b)' v ((a v c) ->3 (b v c))) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7  1wt 8   ->3 wi3 14
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-wom 361  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-i3 46  df-le 129  df-le1 130  df-le2 131  df-c1 132  df-c2 133  df-cmtr 134
This theorem is referenced by: (None)
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