Theorem i3ancom 508

Description: Commutative law for disjunction with Kalmbach implication.

Assertion

Ref	Expression
i3ancom	((a ^ b) ->3 (b ^ a)) = 1

Proof of Theorem i3ancom

Step	Hyp	Ref	Expression
1		i3id 243	. 2 ((b ^ a) ->3 (b ^ a)) = 1
2		ancom 68	. . . 4 (b ^ a) = (a ^ b)
3	2	ri3 245	. . 3 ((b ^ a) ->3 (b ^ a)) = ((a ^ b) ->3 (b ^ a))
4	3	bi1 110	. 2 (((b ^ a) ->3 (b ^ a)) == ((a ^ b) ->3 (b ^ a))) = 1
5	1, 4	wwbmp 197	1 ((a ^ b) ->3 (b ^ a)) = 1

Syntax hints:   = wb 1   ^ wa 7  1wt 9   ->3 wi3 15

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i3 45

metamath.org