Theorem sbequ12r 1713

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 1712	. . 3 |- ( y = x -> ( ph <-> [ x / y ] ph ) )
2	1	bicomd 140	. 2 |- ( y = x -> ( [ x / y ] ph <-> ph ) )
3	2	equcoms 1652	1 |- ( x = y -> ( [ x / y ] ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 104   [wsb 1703

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-4 1455  ax-17 1474  ax-i9 1478

This theorem depends on definitions:  df-bi 116  df-sb 1704

This theorem is referenced by:  abbi  2213  findes  4455  opeliunxp  4532  isarep1  5145  bezoutlemmain  11479