Theorem rbi 90

Description: Introduce biconditional to the right.

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 89	. 2 (c == a) = (c == b)
3		bicom 88	. 2 (a == c) = (c == a)
4		bicom 88	. 2 (b == c) = (c == b)
5	2, 3, 4	3tr1 60	1 (a == c) = (b == c)

Syntax hints:   = wb 1   == tb 5

This theorem is referenced by:  2bi 91  bi1 110  di 118  wwbmp 197  wcon2 200  wwoml2 204  wwoml3 205  wr2 353  wler 373  i3th4 528  mlaconj4 826

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

This theorem depends on definitions:  df-b 38  df-a 39

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