Theorem 19.41vv 1876

Description: Theorem 19.41 of [Margaris] p. 90 with 2 quantifiers. (Contributed by NM, 30-Apr-1995.)

Assertion

Ref	Expression
19.41vv	|- ( E. x E. y ( ph /\ ps ) <-> ( E. x E. y ph /\ ps ) )

Distinct variable groups:   ps, x   ps, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem 19.41vv

Step	Hyp	Ref	Expression
1		19.41v 1875	. . 3 |- ( E. y ( ph /\ ps ) <-> ( E. y ph /\ ps ) )
2	1	exbii 1585	. 2 |- ( E. x E. y ( ph /\ ps ) <-> E. x ( E. y ph /\ ps ) )
3		19.41v 1875	. 2 |- ( E. x ( E. y ph /\ ps ) <-> ( E. x E. y ph /\ ps ) )
4	2, 3	bitri 183	1 |- ( E. x E. y ( ph /\ ps ) <-> ( E. x E. y ph /\ ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   E.wex 1469

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.41vvv  1877  rabxp  4584  rexiunxp  4689  mpomptx  5870  xpassen  6732  dmaddpqlem  7209  nqpi  7210  nqnq0pi  7270  nq0nn  7274