Theorem wed 423

Description: Weak equivalential detachment (WBMP).

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 111	. . 3 1 = (a ≡ b)
3		wed.2	. . 3 (a ≡ b) = (c ≡ d)
4	2, 3	ax-r2 35	. 2 1 = (c ≡ d)
5	4	r3a 422	1 c = d

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

This theorem is referenced by:  r3b 424  i3th4 528

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

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

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