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Theorem 19.3 2191
Description: A wff may be quantified with a variable not free in it. Version of 19.9 2194 with a universal quantifier. Theorem 19.3 of [Margaris] p. 89. See 19.3v 1978 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 2172 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2184 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 208 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wal 1532  wnf 1778
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-12 2167
This theorem depends on definitions:  df-bi 206  df-ex 1775  df-nf 1779
This theorem is referenced by:  19.16  2214  19.17  2215  19.27  2216  19.28  2217  19.37  2221  aaan  2323  axrep4  5284  zfcndrep  10631  bj-alexbiex  36170  bj-alalbial  36172  fvineqsneq  36885
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