Theorem 19.38OLD 1874

Description: Obsolete proof of 19.38 as of 2-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.38OLD	⊢ ((∃xφ → ∀xψ) → ∀x(φ → ψ))

Proof of Theorem 19.38OLD

Step	Hyp	Ref	Expression
1		nfe1 1732	. . 3 ⊢ Ⅎx∃xφ
2		nfa1 1788	. . 3 ⊢ Ⅎx∀xψ
3	1, 2	nfim 1813	. 2 ⊢ Ⅎx(∃xφ → ∀xψ)
4		19.8a 1756	. . 3 ⊢ (φ → ∃xφ)
5		sp 1747	. . 3 ⊢ (∀xψ → ψ)
6	4, 5	imim12i 53	. 2 ⊢ ((∃xφ → ∀xψ) → (φ → ψ))
7	3, 6	alrimi 1765	1 ⊢ ((∃xφ → ∀xψ) → ∀x(φ → ψ))

This proof depends on syntax axioms:   → wi 4  ∀wal 1540  ∃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  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

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

This theorem is used by: (None)