Theorem exlimdvv 1774

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 31-Jul-1995.)

Hypothesis

Ref	Expression
exlimdvv.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
exlimdvv	⊢ (φ → (∃x∃yψ → χ))

Distinct variable groups:   χ,x   φ,x   χ,y   φ,y

Allowed substitution hints:   ψ(x,y)

Proof of Theorem exlimdvv

Step	Hyp	Ref	Expression
1		exlimdvv.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	exlimdv 1697	. 2 ⊢ (φ → (∃yψ → χ))
3	2	exlimdv 1697	1 ⊢ (φ → (∃x∃yψ → χ))

Syntax hints:   → wi 4  ∃wex 1378

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-17 1416

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  euotd  3982  funopg  4877  th3qlem1  6144  fundmen  6222  addnq0mo  6430  mulnq0mo  6431  genprndl  6504  genprndu  6505  genpdisj  6506  mullocpr  6552  addsrmo  6671  mulsrmo  6672