Theorem sbequ6 2388

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

Assertion

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

Proof of Theorem sbequ6

Step	Hyp	Ref	Expression
1		nfnae 2318	. 2 |- F/ z -. A. x x = y
2	1	sbf 2380	1 |- ( [ w / z ] -. A. x x = y <-> -. A. x x = y )

Syntax hints:   -. wn 3   <-> wb 196   A.wal 1481   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)