Theorem sbequ12r 1652

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 1651	. . 3 |- (y = x -> (ph <-> [x / y]ph))
2	1	bicomd 129	. 2 |- (y = x -> ([x / y]ph <-> ph))
3	2	equcoms 1591	1 |- (x = y -> ([x / y]ph <-> ph))

Syntax hints:   -> wi 4   <-> wb 98  [wsb 1642

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420

This theorem depends on definitions:  df-bi 110  df-sb 1643

This theorem is referenced by:  abbi  2148  findes  4269  opeliunxp  4338  isarep1  4928