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Theorem rbi 98
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
StepHypRef Expression
1 rbi.1 . . 3 a = b
21lbi 97 . 2 (c == a) = (c == b)
3 bicom 96 . 2 (a == c) = (c == a)
4 bicom 96 . 2 (b == c) = (c == b)
52, 3, 43tr1 63 1 (a == c) = (b == c)
Colors of variables: term
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
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