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

Theorem truan 1349
Description: True can be removed from a conjunction. (Contributed by FL, 20-Mar-2011.) (Proof shortened by Wolf Lammen, 21-Jul-2019.)
Assertion
Ref Expression
truan ((⊤ ∧ 𝜑) ↔ 𝜑)

Proof of Theorem truan
StepHypRef Expression
1 tru 1336 . . 3
21biantrur 301 . 2 (𝜑 ↔ (⊤ ∧ 𝜑))
32bicomi 131 1 ((⊤ ∧ 𝜑) ↔ 𝜑)
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104  wtru 1333
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-tru 1335
This theorem is referenced by:  truanfal  1381  truxortru  1398  truxorfal  1399
  Copyright terms: Public domain W3C validator