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Theorem 19.27v 1795
Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 3-Jun-2004.)
Assertion
Ref Expression
19.27v (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑𝜓))
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.27v
StepHypRef Expression
1 ax-17 1435 . 2 (𝜓 → ∀𝑥𝜓)
2119.27h 1468 1 (∀𝑥(𝜑𝜓) ↔ (∀𝑥𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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