Theorem drex2 1725

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.)

Hypothesis

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

Assertion

Ref	Expression
drex2	|- ( A. x x = y -> ( E. z ph <-> E. z ps ) )

Proof of Theorem drex2

Step	Hyp	Ref	Expression
1		hbae 1711	. 2 |- ( A. x x = y -> A. z A. x x = y )
2		drex2.1	. 2 |- ( A. x x = y -> ( ph <-> ps ) )
3	1, 2	exbidh 1607	1 |- ( A. x x = y -> ( E. z ph <-> E. z ps ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1346   E.wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exdistrfor  1793