Theorem 2eximi 1650

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 1649	. 2 |- ( E. y ph -> E. y ps )
3	2	eximi 1649	1 |- ( E. x E. y ph -> E. x E. y ps )

Syntax hints:   -> wi 4   E.wex 1541

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-ial 1583

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  excomim  1711  cgsex2g  2840  cgsex4g  2841  vtocl2  2860  vtocl3  2861  dtruarb  4287  opelopabsb  4360  mosubopt  4797  xpmlem  5164  brabvv  6077  ssoprab2i  6120  dmaddpqlem  7640  nqpi  7641  dmaddpq  7642  dmmulpq  7643  enq0sym  7695  enq0ref  7696  enq0tr  7697  nq0nn  7705  prarloc  7766  bj-inex  16606