Theorem wr3 198

Description: Weak R3. (Contributed by NM, 2-Sep-1997.)

Hypothesis

Ref	Expression
wr3.1	(1 ≡ a) = 1

Assertion

Ref	Expression
wr3	a = 1

Proof of Theorem wr3

Step	Hyp	Ref	Expression
1		1b 117	. . 3 (1 ≡ a) = a
2	1	ax-r1 35	. 2 a = (1 ≡ a)
3		wr3.1	. 2 (1 ≡ a) = 1
4	2, 3	ax-r2 36	1 a = 1

Syntax hints:   = wb 1   ≡ tb 5  1wt 8

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42

This theorem is referenced by:  wwbmp  205  wdf-c1  383