Theorem wwbmpr 206

Description: Weak weak equivalential detachment (WBMP). (Contributed by NM, 24-Sep-1997.)

Hypotheses

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

Assertion

Ref	Expression
wwbmpr	a = 1

Proof of Theorem wwbmpr

Step	Hyp	Ref	Expression
1		wwbmpr.1	. 2 b = 1
2		wwbmpr.2	. . 3 (a ≡ b) = 1
3	2	wr1 197	. 2 (b ≡ a) = 1
4	1, 3	wwbmp 205	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:  wr2  371  wlem14  430  ska2  432  ska4  433  i3aa  521  bi3tr  527