Users' Mathboxes Mathbox for Giovanni Mascellani < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  truconj Structured version   Visualization version   GIF version

Theorem truconj 32872
Description: Add true as a conjunct. (Contributed by Giovanni Mascellani, 23-May-2019.)
Assertion
Ref Expression
truconj (𝜑 ↔ (⊤ ∧ 𝜑))

Proof of Theorem truconj
StepHypRef Expression
1 truan 1491 . 2 ((⊤ ∧ 𝜑) ↔ 𝜑)
21bicomi 212 1 (𝜑 ↔ (⊤ ∧ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wa 382  wtru 1475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-an 384  df-tru 1477
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator