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Theorem 19.3 2200
Description: A wff may be quantified with a variable not free in it. Version of 19.9 2203 with a universal quantifier. Theorem 19.3 of [Margaris] p. 89. See 19.3v 1979 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 2181 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2193 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 209 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wal 1535  wnf 1780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-ex 1777  df-nf 1781
This theorem is referenced by:  19.16  2223  19.17  2224  19.27  2225  19.28  2226  19.37  2230  aaan  2332  axrep4  5291  axrep4OLD  5292  zfcndrep  10652  bj-alexbiex  36682  bj-alalbial  36684  fvineqsneq  37395
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