Theorem dral2 1153

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

Hypothesis

Ref	Expression
dral2.1	|- (A.x x = y -> (ph <-> ps))

Assertion

Ref	Expression
dral2	|- (A.x x = y -> (A.zph <-> A.zps))

Proof of Theorem dral2

Step	Hyp	Ref	Expression
1		hbae 1143	. 2 |- (A.x x = y -> A.zA.x x = y)
2		dral2.1	. 2 |- (A.x x = y -> (ph <-> ps))
3	1, 2	albid 1102	1 |- (A.x x = y -> (A.zph <-> A.zps))

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

This theorem is referenced by:  sbal1 1344  ax11eq 1361  ax11el 1362  ax11indalem 1366  ax11inda2ALT 1367  a12lem1 1374  rgen2a 1696  ralcom2 1773  axpownd 4933

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-10 964  ax-12 966  ax-4 971  ax-5o 973  ax-10o 1138

This theorem depends on definitions:  df-bi 147  df-an 225

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