Theorem 19.41vv 1926

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 1925	. . 3 |- ( E. y ( ph /\ ps ) <-> ( E. y ph /\ ps ) )
2	1	exbii 1627	. 2 |- ( E. x E. y ( ph /\ ps ) <-> E. x ( E. y ph /\ ps ) )
3		19.41v 1925	. 2 |- ( E. x ( E. y ph /\ ps ) <-> ( E. x E. y ph /\ ps ) )
4	2, 3	bitri 184	1 |- ( E. x E. y ( ph /\ ps ) <-> ( E. x E. y ph /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1514

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-17 1548  ax-ial 1556

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.41vvv  1927  rabxp  4711  rexiunxp  4819  mpomptx  6035  xpassen  6924  dmaddpqlem  7489  nqpi  7490  nqnq0pi  7550  nq0nn  7554