Theorem u3lem4 740

Description: Lemma for unified implication study.

Assertion

Ref	Expression
u3lem4	(a →3 (a →3 (b →3 a))) = 1

Proof of Theorem u3lem4

Step	Hyp	Ref	Expression
1		lem4 493	. 2 (a →3 (a →3 (b →3 a))) = (a⊥ ∪ (b →3 a))
2		ax-a2 30	. . 3 (a⊥ ∪ (b →3 a)) = ((b →3 a) ∪ a⊥ )
3		u3lemonb 619	. . 3 ((b →3 a) ∪ a⊥ ) = 1
4	2, 3	ax-r2 35	. 2 (a⊥ ∪ (b →3 a)) = 1
5	1, 4	ax-r2 35	1 (a →3 (a →3 (b →3 a))) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ 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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