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))

This proof depends on syntax axioms:   → wi 4  ∃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  ax-17 1616

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

This theorem is used by:  ncfinlower  4484  sfin112  4530  sfindbl  4531  sfinltfin  4536  funsi  5521  fntxp  5805  fnpprod  5844  fundmen  6044  ce0addcnnul  6180  ce0nnulb  6183  ceclb  6184  fce  6189  fnfrec  6321