Theorem wlecon 377

Description: Contrapositive for l.e.

Hypothesis

Ref	Expression
wle.1	(a =<2 b) = 1

Assertion

Ref	Expression
wlecon	(b_|_ =<2 a_|_) = 1

Proof of Theorem wlecon

Step	Hyp	Ref	Expression
1		ax-a2 30	. . . . 5 (b v a) = (a v b)
2	1	bi1 110	. . . 4 ((b v a) == (a v b)) = 1
3		oran 79	. . . . 5 (b v a) = (b_|_ ^ a_|_)_|_
4	3	bi1 110	. . . 4 ((b v a) == (b_|_ ^ a_|_)_|_) = 1
5		wle.1	. . . . 5 (a =<2 b) = 1
6	5	wdf-le2 361	. . . 4 ((a v b) == b) = 1
7	2, 4, 6	w3tr2 357	. . 3 ((b_|_ ^ a_|_)_|_ == b) = 1
8	7	wcon3 201	. 2 ((b_|_ ^ a_|_) == b_|_) = 1
9	8	wdf2le1 367	1 (b_|_ =<2 a_|_) = 1

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7  1wt 9   =<2 wle2 11

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-wom 343

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le 121  df-le1 122  df-le2 123

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