Theorem eeor 795

Description: Rearrange existential quantifiers.

Hypotheses

Ref	Expression
eeor.1	|- (ph -> A.yph)
eeor.2	|- (ps -> A.xps)

Assertion

Ref	Expression
eeor	|- (E.xE.y(ph \/ ps) <-> (E.xph \/ E.yps))

Proof of Theorem eeor

Step	Hyp	Ref	Expression
1		eeor.1	. . . 4 |- (ph -> A.yph)
2	1	19.45 769	. . 3 |- (E.y(ph \/ ps) <-> (ph \/ E.yps))
3	2	biex 733	. 2 |- (E.xE.y(ph \/ ps) <-> E.x(ph \/ E.yps))
4		eeor.2	. . . 4 |- (ps -> A.xps)
5	4	hbex 701	. . 3 |- (E.yps -> A.xE.yps)
6	5	19.44 768	. 2 |- (E.x(ph \/ E.yps) <-> (E.xph \/ E.yps))
7	3, 6	bitr 151	1 |- (E.xE.y(ph \/ ps) <-> (E.xph \/ E.yps))

Syntax hints:   -> wi 2   <-> wb 127   \/ wo 195  A.wal 672  E.wex 678

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679

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