Theorem wcon1 207

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

Hypothesis

Ref	Expression
wcon1.1	(a⊥ ≡ b⊥ ) = 1

Assertion

Ref	Expression
wcon1	(a ≡ b) = 1

Proof of Theorem wcon1

Step	Hyp	Ref	Expression
1		conb 122	. 2 (a ≡ b) = (a⊥ ≡ b⊥ )
2		wcon1.1	. 2 (a⊥ ≡ b⊥ ) = 1
3	1, 2	ax-r2 36	1 (a ≡ b) = 1

This proof depends on syntax axioms:   = wb 1  ^⊥ wn 4   ≡ tb 5  1wt 8

This proof depends on axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

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

This theorem is used by:  wcon3  209  wfh3  425  wfh4  426