Theorem exlimdh 1807

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jan-1997.)

Hypotheses

Ref	Expression
exlimdh.1	⊢ (φ → ∀xφ)
exlimdh.2	⊢ (χ → ∀xχ)
exlimdh.3	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
exlimdh	⊢ (φ → (∃xψ → χ))

Proof of Theorem exlimdh

Step	Hyp	Ref	Expression
1		exlimdh.1	. . 3 ⊢ (φ → ∀xφ)
2	1	nfi 1551	. 2 ⊢ Ⅎxφ
3		exlimdh.2	. . 3 ⊢ (χ → ∀xχ)
4	3	nfi 1551	. 2 ⊢ Ⅎxχ
5		exlimdh.3	. 2 ⊢ (φ → (ψ → χ))
6	2, 4, 5	exlimd 1806	1 ⊢ (φ → (∃xψ → χ))

Syntax hints:   → wi 4  ∀wal 1540  ∃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  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)