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Theorem 19.16 1555
Description: Theorem 19.16 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.16.1 𝑥𝜑
Assertion
Ref Expression
19.16 (∀𝑥(𝜑𝜓) → (𝜑 ↔ ∀𝑥𝜓))

Proof of Theorem 19.16
StepHypRef Expression
1 19.16.1 . . 3 𝑥𝜑
2119.3 1554 . 2 (∀𝑥𝜑𝜑)
3 albi 1468 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
42, 3bitr3id 194 1 (∀𝑥(𝜑𝜓) → (𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105  wal 1351  wnf 1460
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-4 1510
This theorem depends on definitions:  df-bi 117  df-nf 1461
This theorem is referenced by: (None)
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