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Theorem r19.21v 2450
Description: Theorem 19.21 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.21v (∀𝑥𝐴 (𝜑𝜓) ↔ (𝜑 → ∀𝑥𝐴 𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem r19.21v
StepHypRef Expression
1 nfv 1466 . 2 𝑥𝜑
21r19.21 2449 1 (∀𝑥𝐴 (𝜑𝜓) ↔ (𝜑 → ∀𝑥𝐴 𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  wral 2359
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 1381  ax-gen 1383  ax-4 1445  ax-17 1464  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-ral 2364
This theorem is referenced by:  r19.32vdc  2516  rmo4  2806  rmo3  2928  dftr5  3931  reusv3  4273  tfrlem1  6055  tfrlemi1  6079  tfr1onlemaccex  6095  tfrcllemaccex  6108  tfri3  6114  ordiso2  6707  raluz2  9036  ndvdssub  11023  nninfalllem1  11556  nninfsellemqall  11564
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