Theorem i3lor 515

Description: WQL (Weak Quantum Logic) rule.

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 507	. 2 ((c ∪ a) →3 (a ∪ c)) = 1
2		i3lor.1	. . . 4 (a →3 b) = 1
3	2	i3ror 514	. . 3 ((a ∪ c) →3 (b ∪ c)) = 1
4		i3orcom 507	. . 3 ((b ∪ c) →3 (c ∪ b)) = 1
5	3, 4	binr2 500	. 2 ((a ∪ c) →3 (c ∪ b)) = 1
6	1, 5	binr2 500	1 ((c ∪ a) →3 (c ∪ b)) = 1

Syntax hints:   = wb 1   ∪ wo 6  1wt 9   →₃ wi3 15

This theorem is referenced by:  i32or 516  i0i3tr 523

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i3 45  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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