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Theorem 19.21hOLD 2204
Description: Obsolete proof of 19.21h 2107 as of 6-Oct-2021. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.21hOLD.1 (𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
19.21hOLD (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓))

Proof of Theorem 19.21hOLD
StepHypRef Expression
1 19.21hOLD.1 . . 3 (𝜑 → ∀𝑥𝜑)
21nfiOLD 1725 . 2 𝑥𝜑
3219.21OLD 2202 1 (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wal 1473
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:  hbim1OLD  2215
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