Theorem 2eximi 1601

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 1600	. 2 |- ( E. y ph -> E. y ps )
3	2	eximi 1600	1 |- ( E. x E. y ph -> E. x E. y ps )

Syntax hints:   -> wi 4   E.wex 1492

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  excomim  1663  cgsex2g  2774  cgsex4g  2775  vtocl2  2793  vtocl3  2794  dtruarb  4192  opelopabsb  4261  mosubopt  4692  xpmlem  5050  brabvv  5921  ssoprab2i  5964  dmaddpqlem  7376  nqpi  7377  dmaddpq  7378  dmmulpq  7379  enq0sym  7431  enq0ref  7432  enq0tr  7433  nq0nn  7441  prarloc  7502  bj-inex  14662