Theorem i31 520

Description: Theorem for Kalmbach implication. (Contributed by NM, 7-Nov-1997.)

Assertion

Ref	Expression
i31	(a →3 1) = 1

Proof of Theorem i31

Step	Hyp	Ref	Expression
1		df-t 41	. . 3 1 = (a ∪ a⊥ )
2	1	li3 252	. 2 (a →3 1) = (a →3 (a ∪ a⊥ ))
3		bina3 284	. 2 (a →3 (a ∪ a⊥ )) = 1
4	2, 3	ax-r2 36	1 (a →3 1) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ 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

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131

This theorem is referenced by:  i3aa  521  i3th4  546