Theorem drsb2 1228

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).

Assertion

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

Proof of Theorem drsb2

Step	Hyp	Ref	Expression
1		sbequi 1226	. . 3 |- (x = y -> ([x / z]ph -> [y / z]ph))
2	1	a4s 982	. 2 |- (A.x x = y -> ([x / z]ph -> [y / z]ph))
3		sbequi 1226	. . . 4 |- (y = x -> ([y / z]ph -> [x / z]ph))
4	3	equcoms 1128	. . 3 |- (x = y -> ([y / z]ph -> [x / z]ph))
5	4	a4s 982	. 2 |- (A.x x = y -> ([y / z]ph -> [x / z]ph))
6	2, 5	impbid 515	1 |- (A.x x = y -> ([x / z]ph <-> [y / z]ph))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 952   = wceq 954  [wsbc 1168

This theorem is referenced by:  sb9i 1261

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-9 963  ax-10 964  ax-12 966  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-11o 1216

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170

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