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Theorem 19.3 2056
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. See 19.3v 1883 for a version requiring fewer axioms. (Contributed by NM, 12-Mar-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.3.1 𝑥𝜑
Assertion
Ref Expression
19.3 (∀𝑥𝜑𝜑)

Proof of Theorem 19.3
StepHypRef Expression
1 sp 2040 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2052 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 197 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 194  wal 1472  wnf 1698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-12 2033
This theorem depends on definitions:  df-bi 195  df-ex 1695  df-nf 1700
This theorem is referenced by:  19.16  2079  19.17  2080  19.27  2081  19.28  2082  19.37  2086  axrep4  4697  zfcndrep  9292  bj-alexbiex  31670  bj-alalbial  31672  bj-axrep4  31772
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