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Theorem orbile 843
Description: Disjunction of biconditionals.
Assertion
Ref Expression
orbile ((a == c) v (b == c)) =< (((a ^ b) ->2 c) ^ (c ->1 (a v b)))
Proof of Theorem orbile
StepHypRef Expression
1 orbi 842 . 2 ((a == c) v (b == c)) = (((a ->2 c) v (b ->2 c)) ^ ((c ->1 a) v (c ->1 b)))
2 i2or 344 . . 3 ((a ->2 c) v (b ->2 c)) =< ((a ^ b) ->2 c)
3 i1or 345 . . 3 ((c ->1 a) v (c ->1 b)) =< (c ->1 (a v b))
42, 3le2an 169 . 2 (((a ->2 c) v (b ->2 c)) ^ ((c ->1 a) v (c ->1 b))) =< (((a ^ b) ->2 c) ^ (c ->1 (a v b)))
51, 4bltr 138 1 ((a == c) v (b == c)) =< (((a ^ b) ->2 c) ^ (c ->1 (a v b)))
Colors of variables: term
Syntax hints:   =< wle 2   == tb 5   v wo 6   ^ wa 7   ->1 wi1 12   ->2 wi2 13
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-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  mlaconj4  844  mlaconj  845  mlaconjolem  885
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