Theorem i3lor 533

Description: WQL (Weak Quantum Logic) rule. (Contributed by NM, 7-Nov-1997.)

Hypothesis

Ref	Expression
i3lor.1	(a →3 b) = 1

Assertion

Ref	Expression
i3lor	((c ∪ a) →3 (c ∪ b)) = 1

Proof of Theorem i3lor

Step	Hyp	Ref	Expression
1		i3orcom 525	. 2 ((c ∪ a) →3 (a ∪ c)) = 1
2		i3lor.1	. . . 4 (a →3 b) = 1
3	2	i3ror 532	. . 3 ((a ∪ c) →3 (b ∪ c)) = 1
4		i3orcom 525	. . 3 ((b ∪ c) →3 (c ∪ b)) = 1
5	3, 4	binr2 518	. 2 ((a ∪ c) →3 (c ∪ b)) = 1
6	1, 5	binr2 518	1 ((c ∪ a) →3 (c ∪ b)) = 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-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  i32or  534  i0i3tr  541