Theorem 2eximi 1647

Description: Inference adding 2 existential quantifiers to antecedent and consequent. (Contributed by NM, 3-Feb-2005.)

Hypothesis

Ref	Expression
eximi.1	|- ( ph -> ps )

Assertion

Ref	Expression
2eximi	|- ( E. x E. y ph -> E. x E. y ps )

Proof of Theorem 2eximi

Step	Hyp	Ref	Expression
1		eximi.1	. . 3 |- ( ph -> ps )
2	1	eximi 1646	. 2 |- ( E. y ph -> E. y ps )
3	2	eximi 1646	1 |- ( E. x E. y ph -> E. x E. y ps )

Syntax hints:   -> wi 4   E.wex 1538

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-ial 1580

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  excomim  1709  cgsex2g  2836  cgsex4g  2837  vtocl2  2856  vtocl3  2857  dtruarb  4274  opelopabsb  4347  mosubopt  4781  xpmlem  5145  brabvv  6041  ssoprab2i  6084  dmaddpqlem  7552  nqpi  7553  dmaddpq  7554  dmmulpq  7555  enq0sym  7607  enq0ref  7608  enq0tr  7609  nq0nn  7617  prarloc  7678  bj-inex  16200