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Theorem 19.16 1447
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 1446 . 2 (∀𝑥𝜑𝜑)
3 albi 1357 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
42, 3syl5bbr 183 1 (∀𝑥(𝜑𝜓) → (𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1241  wnf 1349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by: (None)
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