Theorem drex2 1732

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 1718	. 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 1614	1 |- ( A. x x = y -> ( E. z ph <-> E. z ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1351   E.wex 1492

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exdistrfor  1800