Theorem wcon3 209

Description: Weak contraposition. (Contributed by NM, 24-Sep-1997.)

Hypothesis

Ref	Expression
wcon3.1	(a⊥ ≡ b) = 1

Assertion

Ref	Expression
wcon3	(a ≡ b⊥ ) = 1

Proof of Theorem wcon3

Step	Hyp	Ref	Expression
1		ax-a1 30	. . . . 5 b = b⊥ ⊥
2	1	ax-r1 35	. . . 4 b⊥ ⊥ = b
3	2	lbi 97	. . 3 (a⊥ ≡ b⊥ ⊥ ) = (a⊥ ≡ b)
4		wcon3.1	. . 3 (a⊥ ≡ b) = 1
5	3, 4	ax-r2 36	. 2 (a⊥ ≡ b⊥ ⊥ ) = 1
6	5	wcon1 207	1 (a ≡ b⊥ ) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5  1wt 8

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

This theorem is referenced by:  wlecon  395  wcomd  418  wfh1  423