Theorem i3orcom 525

Description: Commutative law for conjunction with Kalmbach implication. (Contributed by NM, 7-Nov-1997.)

Assertion

Ref	Expression
i3orcom	((a ∪ b) →3 (b ∪ a)) = 1

Proof of Theorem i3orcom

Step	Hyp	Ref	Expression
1		i3id 251	. 2 ((b ∪ a) →3 (b ∪ a)) = 1
2		ax-a2 31	. . . 4 (b ∪ a) = (a ∪ b)
3	2	ri3 253	. . 3 ((b ∪ a) →3 (b ∪ a)) = ((a ∪ b) →3 (b ∪ a))
4	3	bi1 118	. 2 (((b ∪ a) →3 (b ∪ a)) ≡ ((a ∪ b) →3 (b ∪ a))) = 1
5	1, 4	wwbmp 205	1 ((a ∪ b) →3 (b ∪ a)) = 1

Syntax hints:   = wb 1   ∪ wo 6  1wt 8   →₃ wi3 14

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a4 33  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  df-i3 46

This theorem is referenced by:  i3lor  533