Theorem 2eximdv 1624

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 3-Aug-1995.)

Hypothesis

Ref	Expression
2alimdv.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
2eximdv	⊢ (φ → (∃x∃yψ → ∃x∃yχ))

Distinct variable groups:   φ,x   φ,y

Allowed substitution hints:   ψ(x,y)   χ(x,y)

Proof of Theorem 2eximdv

Step	Hyp	Ref	Expression
1		2alimdv.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	eximdv 1622	. 2 ⊢ (φ → (∃yψ → ∃yχ))
3	2	eximdv 1622	1 ⊢ (φ → (∃x∃yψ → ∃x∃yχ))

Syntax hints:   → wi 4  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  cgsex2g  2892  cgsex4g  2893  spc2egv  2942  spc3egv  2944