Theorem wcon2 208

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 122	. . 3 (a' == b) = (a'' == b')
2		ax-a1 30	. . . . 5 a = a''
3	2	rbi 98	. . . 4 (a == b') = (a'' == b')
4	3	ax-r1 35	. . 3 (a'' == b') = (a == b')
5	1, 4	ax-r2 36	. 2 (a' == b) = (a == b')
6		wcon2.1	. 2 (a == b') = 1
7	5, 6	ax-r2 36	1 (a' == b) = 1

Syntax hints:   = wb 1  'wn 4   == tb 5  1wt 8

This theorem is referenced by:  wcomlem 382  wcomd 418  wcomdr 421  wcom3i 422  wfh1 423  wfh2 424

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-b 39  df-a 40

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