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Theorem 19.17 2225
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 1826 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
2 19.17.1 . . 3 𝑥𝜓
3219.3 2201 . 2 (∀𝑥𝜓𝜓)
41, 3bitrdi 290 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wal 1541  wnf 1791
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-12 2176
This theorem depends on definitions:  df-bi 210  df-ex 1788  df-nf 1792
This theorem is referenced by: (None)
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