Theorem wed 441

Description: Weak equivalential detachment (WBMP). (Contributed by NM, 10-Aug-1997.)

Hypotheses

Ref	Expression
wed.1	a = b
wed.2	(a ≡ b) = (c ≡ d)

Assertion

Ref	Expression
wed	c = d

Proof of Theorem wed

Step	Hyp	Ref	Expression
1		wed.1	. . . 4 a = b
2	1	1bi 119	. . 3 1 = (a ≡ b)
3		wed.2	. . 3 (a ≡ b) = (c ≡ d)
4	2, 3	ax-r2 36	. 2 1 = (c ≡ d)
5	4	r3a 440	1 c = d

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

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439

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

This theorem is referenced by:  r3b  442  i3th4  546