Theorem u3lem14aa2 775

Description: Used to prove →₁ "add antecedent" rule in →₃ system.

Assertion

Ref	Expression
u3lem14aa2	(a →3 (a →3 (b →3 (b →3 a⊥ )⊥ ))) = 1

Proof of Theorem u3lem14aa2

Step	Hyp	Ref	Expression
1		u3lem13a 771	. . . . 5 (b →3 (b →3 a⊥ )⊥ ) = (b →1 a)
2		u3lem13b 772	. . . . . 6 ((b →3 a⊥ ) →3 b⊥ ) = (b →1 a)
3	2	ax-r1 34	. . . . 5 (b →1 a) = ((b →3 a⊥ ) →3 b⊥ )
4	1, 3	ax-r2 35	. . . 4 (b →3 (b →3 a⊥ )⊥ ) = ((b →3 a⊥ ) →3 b⊥ )
5	4	ud3lem0a 252	. . 3 (a →3 (b →3 (b →3 a⊥ )⊥ )) = (a →3 ((b →3 a⊥ ) →3 b⊥ ))
6	5	ud3lem0a 252	. 2 (a →3 (a →3 (b →3 (b →3 a⊥ )⊥ ))) = (a →3 (a →3 ((b →3 a⊥ ) →3 b⊥ )))
7		u3lem14aa 774	. 2 (a →3 (a →3 ((b →3 a⊥ ) →3 b⊥ ))) = 1
8	6, 7	ax-r2 35	1 (a →3 (a →3 (b →3 (b →3 a⊥ )⊥ ))) = 1

Syntax hints:   = wb 1  ^⊥ wn 4  1wt 9   →₁ wi1 13   →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-i1 43  df-i3 45  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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