Theorem sbequ5 1705

Description: Substitution does not change an identical variable specifier. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 21-Dec-2004.)

Assertion

Ref	Expression
sbequ5	|- ( [ w / z ] A. x x = y <-> A. x x = y )

Proof of Theorem sbequ5

Step	Hyp	Ref	Expression
1		nfae 1647	. 2 |- F/ z A. x x = y
2	1	sbf 1700	1 |- ( [ w / z ] A. x x = y <-> A. x x = y )

Syntax hints:   <-> wb 103   A.wal 1282   [wsb 1685

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686

This theorem is referenced by: (None)