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Theorem 19.3 2057
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. See 19.3v 1884 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 2041 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2053 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 198 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 195  wal 1473  wnf 1699
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701
This theorem is referenced by:  19.16  2080  19.17  2081  19.27  2082  19.28  2083  19.37  2087  axrep4  4703  zfcndrep  9315  bj-alexbiex  31877  bj-alalbial  31879  bj-axrep4  31979
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