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Theorem stdpc5OLD 2076
Description: Obsolete proof of stdpc5 2075 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 2018. (Revised by Wolf Lammen, 4-Jul-2021.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
stdpc5.1 𝑥𝜑
Assertion
Ref Expression
stdpc5OLD (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓))

Proof of Theorem stdpc5OLD
StepHypRef Expression
1 stdpc5.1 . 2 𝑥𝜑
2 19.21t 2072 . . 3 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓)))
32biimpd 219 . 2 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓)))
41, 3ax-mp 5 1 (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1480  wnf 1707
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-12 2046
This theorem depends on definitions:  df-bi 197  df-ex 1704  df-nf 1709
This theorem is referenced by: (None)
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