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Theorem 19.21-2OLD 2203
Description: Obsolete proof of 19.21-2 2065 as of 6-Oct-2021. (Contributed by NM, 4-Feb-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
19.21-2OLD.1 𝑥𝜑
19.21-2OLD.2 𝑦𝜑
Assertion
Ref Expression
19.21-2OLD (∀𝑥𝑦(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝑦𝜓))

Proof of Theorem 19.21-2OLD
StepHypRef Expression
1 19.21-2OLD.2 . . . 4 𝑦𝜑
2119.21OLD 2202 . . 3 (∀𝑦(𝜑𝜓) ↔ (𝜑 → ∀𝑦𝜓))
32albii 1737 . 2 (∀𝑥𝑦(𝜑𝜓) ↔ ∀𝑥(𝜑 → ∀𝑦𝜓))
4 19.21-2OLD.1 . . 3 𝑥𝜑
5419.21OLD 2202 . 2 (∀𝑥(𝜑 → ∀𝑦𝜓) ↔ (𝜑 → ∀𝑥𝑦𝜓))
63, 5bitri 263 1 (∀𝑥𝑦(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝑦𝜓))
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: (None)
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