Theorem stdpc5OLD 1799

Description: Obsolete proof of stdpc5 1798 as of 1-Jan-2018. (Contributed by NM, 22-Sep-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
stdpc5.1	⊢ Ⅎxφ

Assertion

Ref	Expression
stdpc5OLD	⊢ (∀x(φ → ψ) → (φ → ∀xψ))

Proof of Theorem stdpc5OLD

Step	Hyp	Ref	Expression
1		stdpc5.1	. . 3 ⊢ Ⅎxφ
2	1	nfri 1762	. 2 ⊢ (φ → ∀xφ)
3		alim 1558	. 2 ⊢ (∀x(φ → ψ) → (∀xφ → ∀xψ))
4	2, 3	syl5 28	1 ⊢ (∀x(φ → ψ) → (φ → ∀xψ))

Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544

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-11 1746

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

This theorem is referenced by: (None)