Theorem eeor 2171

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

Hypotheses

Ref	Expression
eeor.1	|- F/ y ph
eeor.2	|- F/ x ps

Assertion

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

Proof of Theorem eeor

Step	Hyp	Ref	Expression
1		eeor.1	. . . 4 |- F/ y ph
2	1	19.45 2107	. . 3 |- ( E. y ( ph \/ ps ) <-> ( ph \/ E. y ps ) )
3	2	exbii 1774	. 2 |- ( E. x E. y ( ph \/ ps ) <-> E. x ( ph \/ E. y ps ) )
4		eeor.2	. . . 4 |- F/ x ps
5	4	nfex 2154	. . 3 |- F/ x E. y ps
6	5	19.44 2106	. 2 |- ( E. x ( ph \/ E. y ps ) <-> ( E. x ph \/ E. y ps ) )
7	3, 6	bitri 264	1 |- ( E. x E. y ( ph \/ ps ) <-> ( E. x ph \/ E. y ps ) )

Syntax hints:   <-> wb 196   \/ wo 383   E.wex 1704   F/wnf 1708

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-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)