Theorem sbequ6 2032

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 1956	. 2 |- F/z -. A.x x = y
2	1	sbf 2026	1 |- ([w / z] -. A.x x = y <-> -. A.x x = y)

Syntax hints:  -. wn 3   <-> wb 176  A.wal 1540  [wsb 1648

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649

This theorem is referenced by: (None)