Theorem 2eximi 1577

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

Hypothesis

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

Assertion

Ref	Expression
2eximi	|- (E.xE.yph -> E.xE.yps)

Proof of Theorem 2eximi

Step	Hyp	Ref	Expression
1		eximi.1	. . 3 |- (ph -> ps)
2	1	eximi 1576	. 2 |- (E.yph -> E.yps)
3	2	eximi 1576	1 |- (E.xE.yph -> E.xE.yps)

This proof depends on syntax axioms:   -> wi 4  E.wex 1541

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This proof depends on definitions:  df-bi 177  df-ex 1542

This theorem is used by:  excomimOLD  1858  2eu6  2289  cgsex2g  2892  cgsex4g  2893  vtocl2  2911  vtocl3  2912  mosubopt  4613  ssoprab2i  5581  ce0nnulb  6183