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Theorem 19.28OLD 2223
 Description: Obsolete proof of 19.28 2083 as of 6-Oct-2021. (Contributed by NM, 1-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.28OLD.1 𝑥𝜑
Assertion
Ref Expression
19.28OLD (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))

Proof of Theorem 19.28OLD
StepHypRef Expression
1 19.26 1786 . 2 (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑥𝜓))
2 19.28OLD.1 . . . 4 𝑥𝜑
3219.3OLD 2190 . . 3 (∀𝑥𝜑𝜑)
43anbi1i 727 . 2 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
51, 4bitri 263 1 (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   ∧ wa 383  ∀wal 1473  ℲwnfOLD 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-12 2034 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nfOLD 1712 This theorem is referenced by:  nfan1OLD  2224
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