Theorem sbequ12r 1820

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 1819	. . 3 |- ( y = x -> ( ph <-> [ x / y ] ph ) )
2	1	bicomd 141	. 2 |- ( y = x -> ( [ x / y ] ph <-> ph ) )
3	2	equcoms 1756	1 |- ( x = y -> ( [ x / y ] ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 105   [wsb 1810

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 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578

This theorem depends on definitions:  df-bi 117  df-sb 1811

This theorem is referenced by:  abbi  2345  findes  4701  opeliunxp  4781  isarep1  5416  bezoutlemmain  12568