Theorem drex1 1152

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint).

Hypothesis

Ref	Expression
drex1.1	|- (A.x x = y -> (ph <-> ps))

Assertion

Ref	Expression
drex1	|- (A.x x = y -> (E.xph <-> E.yps))

Proof of Theorem drex1

Step	Hyp	Ref	Expression
1		drex1.1	. . . . 5 |- (A.x x = y -> (ph <-> ps))
2	1	negbid 609	. . . 4 |- (A.x x = y -> (-. ph <-> -. ps))
3	2	dral1 1150	. . 3 |- (A.x x = y -> (A.x -. ph <-> A.y -. ps))
4	3	negbid 609	. 2 |- (A.x x = y -> (-. A.x -. ph <-> -. A.y -. ps))
5		df-ex 978	. 2 |- (E.xph <-> -. A.x -. ph)
6		df-ex 978	. 2 |- (E.yps <-> -. A.y -. ps)
7	4, 5, 6	3bitr4g 553	1 |- (A.x x = y -> (E.xph <-> E.yps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146  A.wal 951   = wceq 953  E.wex 977

This theorem is referenced by:  drsb1 1171  dfid3 2826

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-10 963  ax-12 965  ax-4 970  ax-5o 972  ax-10o 1136

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978

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