Theorem sbequ12r 1655

Description: An equality theorem for substitution. (Contributed by NM, 6-Oct-2004.) (Proof shortened by Andrew Salmon, 21-Jun-2011.)

Assertion

Ref	Expression
sbequ12r	|- ( x = y -> ( [ x / y ] ph <-> ph ) )

Proof of Theorem sbequ12r

Step	Hyp	Ref	Expression
1		sbequ12 1654	. . 3 |- ( y = x -> ( ph <-> [ x / y ] ph ) )
2	1	bicomd 129	. 2 |- ( y = x -> ( [ x / y ] ph <-> ph ) )
3	2	equcoms 1594	1 |- ( x = y -> ( [ x / y ] ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 98   [wsb 1645

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423

This theorem depends on definitions:  df-bi 110  df-sb 1646

This theorem is referenced by:  abbi  2151  findes  4326  opeliunxp  4395  isarep1  4985