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Theorem 19.17 2132
Description: Theorem 19.17 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.17.1 𝑥𝜓
Assertion
Ref Expression
19.17 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))

Proof of Theorem 19.17
StepHypRef Expression
1 albi 1786 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
2 19.17.1 . . 3 𝑥𝜓
3219.3 2107 . 2 (∀𝑥𝜓𝜓)
41, 3syl6bb 276 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1521  wnf 1748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745  df-nf 1750
This theorem is referenced by: (None)
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