Theorem i3ror 532

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

Hypothesis

Ref	Expression
i3ror.1	(a →3 b) = 1

Assertion

Ref	Expression
i3ror	((a ∪ c) →3 (b ∪ c)) = 1

Proof of Theorem i3ror

Step	Hyp	Ref	Expression
1		i3ror.1	. . 3 (a →3 b) = 1
2		bina3 284	. . 3 (b →3 (b ∪ c)) = 1
3	1, 2	binr2 518	. 2 (a →3 (b ∪ c)) = 1
4		bina4 285	. 2 (c →3 (b ∪ c)) = 1
5	3, 4	binr3 519	1 ((a ∪ c) →3 (b ∪ c)) = 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:  i3lor  533  i32or  534  i3ran  535  i3i0tr  542