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Theorem 19.17 1489
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 1398 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
2 19.17.1 . . 3 𝑥𝜓
3219.3 1487 . 2 (∀𝑥𝜓𝜓)
41, 3syl6bb 194 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  wal 1283  wnf 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by: (None)
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