Theorem sbequ5 1770

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 1707	. 2 |- F/ z A. x x = y
2	1	sbf 1765	1 |- ( [ w / z ] A. x x = y <-> A. x x = y )

Syntax hints:   <-> wb 104   A.wal 1341   [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-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751

This theorem is referenced by: (None)