Theorem eeor 1585

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 1573	. . 3 |- ( E. y ( ph \/ ps ) <-> ( ph \/ E. y ps ) )
3	2	exbii 1496	. 2 |- ( E. x E. y ( ph \/ ps ) <-> E. x ( ph \/ E. y ps ) )
4		eeor.2	. . . 4 |- F/ x ps
5	4	nfex 1528	. . 3 |- F/ x E. y ps
6	5	19.44 1572	. 2 |- ( E. x ( ph \/ E. y ps ) <-> ( E. x ph \/ E. y ps ) )
7	3, 6	bitri 173	1 |- ( E. x E. y ( ph \/ ps ) <-> ( E. x ph \/ E. y ps ) )

Syntax hints:   <-> wb 98   \/ wo 629   F/wnf 1349   E.wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by: (None)