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Theorem 19.23ht 1402
Description: Closed form of Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 7-Nov-2005.) (Revised by Mario Carneiro, 1-Feb-2015.)
Assertion
Ref Expression
19.23ht (∀𝑥(𝜓 → ∀𝑥𝜓) → (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓)))

Proof of Theorem 19.23ht
StepHypRef Expression
1 ax-ie2 1399 1 (∀𝑥(𝜓 → ∀𝑥𝜓) → (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  wal 1257  wex 1397
This theorem was proved from axioms:  ax-ie2 1399
This theorem is referenced by:  19.23h  1403  exlimd2  1502  19.9ht  1548
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