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Theorem 19.3 1489
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 1444 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nfri 1455 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 124 1 (∀𝑥𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 103  wal 1285  wnf 1392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-4 1443
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  19.16  1490  19.17  1491  19.27  1496  19.28  1498  19.37-1  1607  rexxfrd  4258
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