Theorem eeor 1885

Description: Rearrange existential quantifiers. (Contributed by NM, 8-Aug-1994.)

Hypotheses

Ref	Expression
eeor.1	|- F/yph
eeor.2	|- F/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 |- F/yph
2	1	19.45 1878	. . 3 |- (E.y(ph \/ ps) <-> (ph \/ E.yps))
3	2	exbii 1582	. 2 |- (E.xE.y(ph \/ ps) <-> E.x(ph \/ E.yps))
4		eeor.2	. . . 4 |- F/xps
5	4	nfex 1843	. . 3 |- F/xE.yps
6	5	19.44 1877	. 2 |- (E.x(ph \/ E.yps) <-> (E.xph \/ E.yps))
7	3, 6	bitri 240	1 |- (E.xE.y(ph \/ ps) <-> (E.xph \/ E.yps))

Syntax hints:   <-> wb 176   \/ wo 357  E.wex 1541   F/wnf 1544

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-6 1729  ax-7 1734  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)