Theorem i3ancom 526

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

Assertion

Ref	Expression
i3ancom	((a ∩ b) →3 (b ∩ a)) = 1

Proof of Theorem i3ancom

Step	Hyp	Ref	Expression
1		i3id 251	. 2 ((b ∩ a) →3 (b ∩ a)) = 1
2		ancom 74	. . . 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

This proof depends on syntax axioms:   = wb 1   ∩ wa 7  1wt 8   →₃ wi3 14

This proof depends on 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 proof depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46

This theorem is used by: (None)