Theorem sbequ6 1793

Description: Substitution does not change a distinctor. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 14-May-2005.)

Assertion

Ref	Expression
sbequ6	|- ( [ w / z ] -. A. x x = y <-> -. A. x x = y )

Proof of Theorem sbequ6

Step	Hyp	Ref	Expression
1		nfnae 1732	. 2 |- F/ z -. A. x x = y
2	1	sbf 1787	1 |- ( [ w / z ] -. A. x x = y <-> -. A. x x = y )

Syntax hints:   -. wn 3   <-> wb 105   A.wal 1361   [wsb 1772

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-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773

This theorem is referenced by: (None)