Theorem sbequ12r 1765

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 1764	. . 3 |- ( y = x -> ( ph <-> [ x / y ] ph ) )
2	1	bicomd 140	. 2 |- ( y = x -> ( [ x / y ] ph <-> ph ) )
3	2	equcoms 1701	1 |- ( x = y -> ( [ x / y ] ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 104   [wsb 1755

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 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523

This theorem depends on definitions:  df-bi 116  df-sb 1756

This theorem is referenced by:  abbi  2284  findes  4587  opeliunxp  4666  isarep1  5284  bezoutlemmain  11953