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Theorem 19.21OLD 2202
Description: Obsolete proof of 19.21 2062 as of 6-Oct-2021. (Contributed by NM, 14-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.21OLD.1 𝑥𝜑
Assertion
Ref Expression
19.21OLD (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓))

Proof of Theorem 19.21OLD
StepHypRef Expression
1 19.21OLD.1 . 2 𝑥𝜑
2 19.21tOLD 2201 . 2 (Ⅎ𝑥𝜑 → (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓)))
31, 2ax-mp 5 1 (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wal 1473  wnfOLD 1700
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-10 2006  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712
This theorem is referenced by:  19.21-2OLD  2203  19.21hOLD  2204
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