Theorem rbi 98

Description: Introduce biconditional to the right. (Contributed by NM, 10-Aug-1997.)

Hypothesis

Ref	Expression
rbi.1	a = b

Assertion

Ref	Expression
rbi	(a ≡ c) = (b ≡ c)

Proof of Theorem rbi

Step	Hyp	Ref	Expression
1		rbi.1	. . 3 a = b
2	1	lbi 97	. 2 (c ≡ a) = (c ≡ b)
3		bicom 96	. 2 (a ≡ c) = (c ≡ a)
4		bicom 96	. 2 (b ≡ c) = (c ≡ b)
5	2, 3, 4	3tr1 63	1 (a ≡ c) = (b ≡ c)

Syntax hints:   = wb 1   ≡ tb 5

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

This theorem depends on definitions:  df-b 39  df-a 40

This theorem is referenced by:  2bi  99  bi1  118  di  126  wwbmp  205  wcon2  208  wwoml2  212  wwoml3  213  wr2  371  wler  391  i3th4  546  mlaconj4  844