Theorem dral2-o 2181

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 1966 using ax-10o 2139. (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.zph <-> A.zps))

Proof of Theorem dral2-o

Step	Hyp	Ref	Expression
1		hbae-o 2153	. 2 |- (A.x x = y -> A.zA.x x = y)
2		dral2-o.1	. 2 |- (A.x x = y -> (ph <-> ps))
3	1, 2	albidh 1590	1 |- (A.x x = y -> (A.zph <-> A.zps))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-7 1734  ax-4 2135  ax-5o 2136  ax-6o 2137  ax-10o 2139  ax-12o 2142

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  ax11eq  2193  ax11el  2194  ax11indalem  2197  ax11inda2ALT  2198