Theorem dral2-o 34215

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). Version of dral2 2324 using ax-c11 34172. (Contributed by NM, 27-Feb-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

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

Proof of Theorem dral2-o

Step	Hyp	Ref	Expression
1		hbae-o 34188	. 2 |- ( A. x x = y -> A. z A. x x = y )
2		dral2-o.1	. 2 |- ( A. x x = y -> ( ph <-> ps ) )
3	1, 2	albidh 1793	1 |- ( A. x x = y -> ( A. z ph <-> A. z ps ) )

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

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-11 2034  ax-c5 34168  ax-c4 34169  ax-c7 34170  ax-c10 34171  ax-c11 34172  ax-c9 34175

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  ax12eq  34226  ax12el  34227  ax12indalem  34230  ax12inda2ALT  34231