Theorem wwbmp 205

Description: Weak weak equivalential detachment (WBMP). (Contributed by NM, 2-Sep-1997.)

Hypotheses

Ref	Expression
wwbmp.1	a = 1
wwbmp.2	(a ≡ b) = 1

Assertion

Ref	Expression
wwbmp	b = 1

Proof of Theorem wwbmp

Step	Hyp	Ref	Expression
1		wwbmp.1	. . . . 5 a = 1
2	1	rbi 98	. . . 4 (a ≡ b) = (1 ≡ b)
3	2	ax-r1 35	. . 3 (1 ≡ b) = (a ≡ b)
4		wwbmp.2	. . 3 (a ≡ b) = 1
5	3, 4	ax-r2 36	. 2 (1 ≡ b) = 1
6	5	wr3 198	1 b = 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:  wwbmpr  206  bina1  282  bina2  283  wr2  371  ska2  432  i3abs2  523  i3orcom  525  i3ancom  526  i3btr  528  wdid0id5  1111  wdid0id1  1112  wdid0id2  1113  wdid0id3  1114  wdid0id4  1115