Theorem wwbmp 197

Description: Weak weak equivalential detachment (WBMP).

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 90	. . . 4 (a ≡ b) = (1 ≡ b)
3	2	ax-r1 34	. . 3 (1 ≡ b) = (a ≡ b)
4		wwbmp.2	. . 3 (a ≡ b) = 1
5	3, 4	ax-r2 35	. 2 (1 ≡ b) = 1
6	5	wr3 190	1 b = 1

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

This theorem is referenced by:  wwbmpr 198  bina1 274  bina2 275  wr2 353  ska2 414  i3abs2 505  i3orcom 507  i3ancom 508  i3btr 510

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

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