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Theorem 19.3 2204
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. See 19.3v 2051 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 2188 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2200 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 199 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1618  wnf 1845
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1859  ax-4 1874  ax-5 1976  ax-6 2042  ax-7 2078  ax-12 2184
This theorem depends on definitions:  df-bi 197  df-ex 1842  df-nf 1847
This theorem is referenced by:  19.16  2228  19.17  2229  19.27  2230  19.28  2231  19.37  2235  axrep4  4915  zfcndrep  9599  bj-alexbiex  32967  bj-alalbial  32969  bj-axrep4  33068
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