Theorem sbequ12r 1818

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 1817	. . 3 |- ( y = x -> ( ph <-> [ x / y ] ph ) )
2	1	bicomd 141	. 2 |- ( y = x -> ( [ x / y ] ph <-> ph ) )
3	2	equcoms 1754	1 |- ( x = y -> ( [ x / y ] ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 105   [wsb 1808

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-4 1556  ax-17 1572  ax-i9 1576

This theorem depends on definitions:  df-bi 117  df-sb 1809

This theorem is referenced by:  abbi  2343  findes  4694  opeliunxp  4773  isarep1  5406  bezoutlemmain  12514