Theorem drsb2 2061

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.)

Assertion

Ref	Expression
drsb2	|- (A.x x = y -> ([x / z]ph <-> [y / z]ph))

Proof of Theorem drsb2

Step	Hyp	Ref	Expression
1		sbequ 2060	. 2 |- (x = y -> ([x / z]ph <-> [y / z]ph))
2	1	sps 1754	1 |- (A.x x = y -> ([x / z]ph <-> [y / z]ph))

Syntax hints:   -> wi 4   <-> 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649

This theorem is referenced by:  sb9i  2094