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Theorem wler 391
Description: Add disjunct to right of l.e.
Hypothesis
Ref Expression
wle.1 (a =<2 b) = 1
Assertion
Ref Expression
wler (a =<2 (b v c)) = 1
Proof of Theorem wler
StepHypRef Expression
1 df-le 129 . 2 (a =<2 (b v c)) = ((a v (b v c)) == (b v c))
2 ax-a3 32 . . . . 5 ((a v b) v c) = (a v (b v c))
32ax-r1 35 . . . 4 (a v (b v c)) = ((a v b) v c)
43rbi 98 . . 3 ((a v (b v c)) == (b v c)) = (((a v b) v c) == (b v c))
5 df-le 129 . . . . . 6 (a =<2 b) = ((a v b) == b)
65ax-r1 35 . . . . 5 ((a v b) == b) = (a =<2 b)
7 wle.1 . . . . 5 (a =<2 b) = 1
86, 7ax-r2 36 . . . 4 ((a v b) == b) = 1
98wr5-2v 366 . . 3 (((a v b) v c) == (b v c)) = 1
104, 9ax-r2 36 . 2 ((a v (b v c)) == (b v c)) = 1
111, 10ax-r2 36 1 (a =<2 (b v c)) = 1
Colors of variables: term
Syntax hints:   = wb 1   == tb 5   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: (None)
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