Theorem i32or 516

Description: WQL (Weak Quantum Logic) rule.

Hypotheses

Ref	Expression
i32or.1	(a →3 b) = 1
i32or.2	(c →3 d) = 1

Assertion

Ref	Expression
i32or	((a ∪ c) →3 (b ∪ d)) = 1

Proof of Theorem i32or

Step	Hyp	Ref	Expression
1		i32or.1	. . 3 (a →3 b) = 1
2	1	i3ror 514	. 2 ((a ∪ c) →3 (b ∪ c)) = 1
3		i32or.2	. . 3 (c →3 d) = 1
4	3	i3lor 515	. 2 ((b ∪ c) →3 (b ∪ d)) = 1
5	2, 4	binr2 500	1 ((a ∪ c) →3 (b ∪ d)) = 1

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

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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