Theorem sbequ5 1793

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 1730	. 2 |- F/ z A. x x = y
2	1	sbf 1788	1 |- ( [ w / z ] A. x x = y <-> A. x x = y )

Syntax hints:   <-> wb 105   A.wal 1362   [wsb 1773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774

This theorem is referenced by: (None)