Theorem u3lem5 745

Description: Lemma for unified implication study.

Assertion

Ref	Expression
u3lem5	(a →3 (a →3 b)) = (a⊥ ∪ b)

Proof of Theorem u3lem5

Step	Hyp	Ref	Expression
1		comi31 490	. . 3 a C (a →3 b)
2	1	u3lemc4 685	. 2 (a →3 (a →3 b)) = (a⊥ ∪ (a →3 b))
3		ax-a2 30	. . 3 (a⊥ ∪ (a →3 b)) = ((a →3 b) ∪ a⊥ )
4		u3lemona 609	. . 3 ((a →3 b) ∪ a⊥ ) = (a⊥ ∪ b)
5	3, 4	ax-r2 35	. 2 (a⊥ ∪ (a →3 b)) = (a⊥ ∪ b)
6	2, 5	ax-r2 35	1 (a →3 (a →3 b)) = (a⊥ ∪ b)

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   →₃ wi3 15

This theorem is referenced by:  u3lem6 749  u3lem14mp 776

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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