Theorem stdpc5OLD 2064

Description: Obsolete proof of stdpc5 2063 as of 11-Oct-2021. (Contributed by NM, 22-Sep-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) Remove dependency on ax-10 2006. (Revised by Wolf Lammen, 4-Jul-2021.) (New usage is discouraged.) (Proof modification 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	. 2 ⊢ Ⅎ𝑥𝜑
2		19.21t 2061	. . 3 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) ↔ (𝜑 → ∀𝑥𝜓)))
3	2	biimpd 218	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))
4	1, 3	ax-mp 5	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1473  Ⅎwnf 1699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)