Theorem drex2 1157

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
drex2.1	|- (A.x x = y -> (ph <-> ps))

Assertion

Ref	Expression
drex2	|- (A.x x = y -> (E.zph <-> E.zps))

Proof of Theorem drex2

Step	Hyp	Ref	Expression
1		hbae 1145	. 2 |- (A.x x = y -> A.zA.x x = y)
2		drex2.1	. 2 |- (A.x x = y -> (ph <-> ps))
3	1, 2	exbid 1105	1 |- (A.x x = y -> (E.zph <-> E.zps))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 954   = wceq 956  E.wex 980

This theorem is referenced by:  dfid3 2836

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-10o 1140

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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