Theorem dral2 1745

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
dral2.1	|- ( A. x x = y -> ( ph <-> ps ) )

Assertion

Ref	Expression
dral2	|- ( A. x x = y -> ( A. z ph <-> A. z ps ) )

Proof of Theorem dral2

Step	Hyp	Ref	Expression
1		hbae 1732	. 2 |- ( A. x x = y -> A. z A. x x = y )
2		dral2.1	. 2 |- ( A. x x = y -> ( ph <-> ps ) )
3	1, 2	albidh 1494	1 |- ( A. x x = y -> ( A. z ph <-> A. z ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1362

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 1461  ax-7 1462  ax-gen 1463  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  drnf2  1748  equveli  1773  drnfc1  2356  drnfc2  2357