Theorem sbequ12r 1760

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 1759	. . 3 |- ( y = x -> ( ph <-> [ x / y ] ph ) )
2	1	bicomd 140	. 2 |- ( y = x -> ( [ x / y ] ph <-> ph ) )
3	2	equcoms 1696	1 |- ( x = y -> ( [ x / y ] ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 104   [wsb 1750

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518

This theorem depends on definitions:  df-bi 116  df-sb 1751

This theorem is referenced by:  abbi  2280  findes  4580  opeliunxp  4659  isarep1  5274  bezoutlemmain  11931