Theorem drex2 2328

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
dral1.1	|- ( 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 2315	. 2 |- ( A. x x = y -> A. z A. x x = y )
2		dral1.1	. 2 |- ( A. x x = y -> ( ph <-> ps ) )
3	1, 2	exbidh 1794	1 |- ( A. x x = y -> ( E. z ph <-> E. z ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by:  dfid3  5025  dropab1  38651  dropab2  38652  e2ebind  38779