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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 𝑥𝜑
Assertion
Ref Expression
stdpc5OLD (∀𝑥(𝜑𝜓) → (𝜑 → ∀𝑥𝜓))

Proof of Theorem stdpc5OLD
StepHypRef Expression
1 stdpc5.1 . 2 𝑥𝜑
2 19.21t 2061 . . 3 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓)))
32biimpd 218 . 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 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)
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