ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.16 GIF version

Theorem 19.16 1488
Description: Theorem 19.16 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.16.1 𝑥𝜑
Assertion
Ref Expression
19.16 (∀𝑥(𝜑𝜓) → (𝜑 ↔ ∀𝑥𝜓))

Proof of Theorem 19.16
StepHypRef Expression
1 19.16.1 . . 3 𝑥𝜑
2119.3 1487 . 2 (∀𝑥𝜑𝜑)
3 albi 1398 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
42, 3syl5bbr 192 1 (∀𝑥(𝜑𝜓) → (𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  wal 1283  wnf 1390
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-5 1377  ax-gen 1379  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator