Theorem lem3.3.2 1046

Description: Equation 3.2 of [PavMeg1999] p. 9. (Contributed by Roy F. Longton, 27-Jun-2005.) (Revised by Roy F. Longton, 3-Jul-2005.)

Hypotheses

Ref	Expression
lem3.3.2.1	a = 1
lem3.3.2.2	(a →0 b) = 1

Assertion

Ref	Expression
lem3.3.2	b = 1

Proof of Theorem lem3.3.2

Step	Hyp	Ref	Expression
1		lem3.3.2.1	. 2 a = 1
2		df-i0 43	. . . 4 (a →0 b) = (a⊥ ∪ b)
3	2	ax-r1 35	. . 3 (a⊥ ∪ b) = (a →0 b)
4		lem3.3.2.2	. . 3 (a →0 b) = 1
5	3, 4	ax-r2 36	. 2 (a⊥ ∪ b) = 1
6	1, 5	skr0 242	1 b = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6  1wt 8   →₀ wi0 11

This theorem was proved from axioms:  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-t 41  df-f 42  df-i0 43

This theorem is referenced by:  lem3.3.5  1055