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Theorem wle2or 403
Description: Disjunction of 2 l.e.'s.
Hypotheses
Ref Expression
wle2.1 (a =<2 b) = 1
wle2.2 (c =<2 d) = 1
Assertion
Ref Expression
wle2or ((a v c) =<2 (b v d)) = 1
Proof of Theorem wle2or
StepHypRef Expression
1 wle2.1 . . 3 (a =<2 b) = 1
21wleror 393 . 2 ((a v c) =<2 (b v c)) = 1
3 wle2.2 . . . 4 (c =<2 d) = 1
43wleror 393 . . 3 ((c v b) =<2 (d v b)) = 1
5 ax-a2 31 . . . 4 (b v c) = (c v b)
65bi1 118 . . 3 ((b v c) == (c v b)) = 1
7 ax-a2 31 . . . 4 (b v d) = (d v b)
87bi1 118 . . 3 ((b v d) == (d v b)) = 1
94, 6, 8wle3tr1 399 . 2 ((b v c) =<2 (b v d)) = 1
102, 9wletr 396 1 ((a v c) =<2 (b v d)) = 1
Colors of variables: term
Syntax hints:   = wb 1   v wo 6  1wt 8   =<2 wle2 10
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
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131
This theorem is referenced by:  wledi  405  wledio  406
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