Theorem wwbmpr 198

Description: Weak weak equivalential detachment (WBMP).

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 189	. 2 (b == a) = 1
4	1, 3	wwbmp 197	1 a = 1

Syntax hints:   = wb 1   == tb 5  1wt 9

This theorem is referenced by:  wr2 353  wlem14 412  ska2 414  ska4 415  i3aa 503  bi3tr 509

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41

metamath.org