ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.3 GIF version

Theorem 19.3 1514
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 1469 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nfri 1480 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 125 1 (∀𝑥𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wal 1310  wnf 1417
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-4 1468
This theorem depends on definitions:  df-bi 116  df-nf 1418
This theorem is referenced by:  19.16  1515  19.17  1516  19.27  1521  19.28  1523  19.37-1  1633  rexxfrd  4342
  Copyright terms: Public domain W3C validator