Theorem wa6 196

Description: Weak A6. (Contributed by NM, 12-Jul-1998.)

Assertion

Ref	Expression
wa6	((a ≡ b) ≡ ((a⊥ ∪ b⊥ )⊥ ∪ (a ∪ b)⊥ )) = 1

Proof of Theorem wa6

Step	Hyp	Ref	Expression
1		df-b 39	. 2 (a ≡ b) = ((a⊥ ∪ b⊥ )⊥ ∪ (a ∪ b)⊥ )
2	1	bi1 118	1 ((a ≡ b) ≡ ((a⊥ ∪ b⊥ )⊥ ∪ (a ∪ b)⊥ )) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6  1wt 8

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42

This theorem is referenced by: (None)