Theorem i32an 519

Description: WQL (Weak Quantum Logic) rule.

Hypotheses

Ref	Expression
i32an.1	(a ->3 b) = 1
i32an.2	(c ->3 d) = 1

Assertion

Ref	Expression
i32an	((a ^ c) ->3 (b ^ d)) = 1

Proof of Theorem i32an

Step	Hyp	Ref	Expression
1		i32an.1	. . 3 (a ->3 b) = 1
2	1	i3ran 517	. 2 ((a ^ c) ->3 (b ^ c)) = 1
3		i32an.2	. . 3 (c ->3 d) = 1
4	3	i3lan 518	. 2 ((b ^ c) ->3 (b ^ d)) = 1
5	2, 4	binr2 500	1 ((a ^ c) ->3 (b ^ d)) = 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-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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