Theorem lem3.4.4 1077

Description: Equation 3.12 of [PavMeg1999] p. 9. (Contributed by Roy F. Longton, 29-Jun-2005.) (Revised by Roy F. Longton, 3-Jul-2005.)

Hypotheses

Ref	Expression
lem3.4.4.1	(a →2 b) = 1
lem3.4.4.2	(b →2 a) = 1

Assertion

Ref	Expression
lem3.4.4	(a ≡5 b) = 1

Proof of Theorem lem3.4.4

Step	Hyp	Ref	Expression
1		lem3.4.4.2	. . . 4 (b →2 a) = 1
2	1	lem3.3.4 1053	. . 3 (a →2 (a ≡5 b)) = (a ≡5 b)
3	2	ax-r1 35	. 2 (a ≡5 b) = (a →2 (a ≡5 b))
4		lem3.4.4.1	. . 3 (a →2 b) = 1
5	4	lem3.4.3 1076	. 2 (a →2 (a ≡5 b)) = 1
6	3, 5	ax-r2 36	1 (a ≡5 b) = 1

Syntax hints:   = wb 1  1wt 8   →₂ wi2 13   ≡₅ wid5 22

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  ax-wom 361

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131  df-id5 1047

This theorem is referenced by:  lem3.4.6  1079