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Theorem 19.3 1564
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-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 1521 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nfri 1529 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 126 1 (∀𝑥𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 105  wal 1361  wnf 1470
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-4 1520
This theorem depends on definitions:  df-bi 117  df-nf 1471
This theorem is referenced by:  19.16  1565  19.17  1566  19.27  1571  19.28  1573  19.37-1  1684  rexxfrd  4477
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