Theorem exlimdvv 1637

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 1636	. 2 ⊢ (φ → (∃yψ → χ))
3	2	exlimdv 1636	1 ⊢ (φ → (∃x∃yψ → χ))

Syntax hints:   → wi 4  ∃wex 1541

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616

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

This theorem is referenced by:  ncfinlower  4483  sfin112  4529  sfindbl  4530  sfinltfin  4535  funsi  5520  fntxp  5804  fnpprod  5843  fundmen  6043  ce0addcnnul  6179  ce0nnulb  6182  ceclb  6183  fce  6188  fnfrec  6320