Theorem sbequ12r 1695

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 1694	. . 3 |- ( y = x -> ( ph <-> [ x / y ] ph ) )
2	1	bicomd 139	. 2 |- ( y = x -> ( [ x / y ] ph <-> ph ) )
3	2	equcoms 1634	1 |- ( x = y -> ( [ x / y ] ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 103   [wsb 1685

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463

This theorem depends on definitions:  df-bi 115  df-sb 1686

This theorem is referenced by:  abbi  2192  findes  4344  opeliunxp  4413  isarep1  5005  bezoutlemmain  10387