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Theorem 19.3 2204
Description: A wff may be quantified with a variable not free in it. Version of 19.9 2207 with a universal quantifier. Theorem 19.3 of [Margaris] p. 89. See 19.3v 1987 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 2184 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2197 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 212 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wal 1536  wnf 1785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-ex 1782  df-nf 1786
This theorem is referenced by:  19.16  2229  19.17  2230  19.27  2231  19.28  2232  19.37  2236  axrep4  5181  zfcndrep  10034  bj-alexbiex  34093  bj-alalbial  34095  fvineqsneq  34777
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