Theorem drex2 1742

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 1728	. 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 1624	1 |- ( A. x x = y -> ( E. z ph <-> E. z ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1361   E.wex 1502

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exdistrfor  1810