Theorem wcon2 200

Description: Weak contraposition.

Hypothesis

Ref	Expression
wcon2.1	(a == b_|_) = 1

Assertion

Ref	Expression
wcon2	(a_|_ == b) = 1

Proof of Theorem wcon2

Step	Hyp	Ref	Expression
1		conb 114	. . 3 (a_|_ == b) = (a_|__|_ == b_|_)
2		ax-a1 29	. . . . 5 a = a_|__|_
3	2	rbi 90	. . . 4 (a == b_|_) = (a_|__|_ == b_|_)
4	3	ax-r1 34	. . 3 (a_|__|_ == b_|_) = (a == b_|_)
5	1, 4	ax-r2 35	. 2 (a_|_ == b) = (a == b_|_)
6		wcon2.1	. 2 (a == b_|_) = 1
7	5, 6	ax-r2 35	1 (a_|_ == b) = 1

Syntax hints:   = wb 1  _|_wn 4   == tb 5  1wt 9

This theorem is referenced by:  wcomlem 364  wcomd 400  wcomdr 403  wcom3i 404  wfh1 405  wfh2 406

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-b 38  df-a 39

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