Theorem sbequ5 1756

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 1698	. 2 |- F/ z A. x x = y
2	1	sbf 1751	1 |- ( [ w / z ] A. x x = y <-> A. x x = y )

Syntax hints:   <-> wb 104   A.wal 1330   [wsb 1736

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737

This theorem is referenced by: (None)