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Theorem truan 1276
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 1263 . . 3
21biantrur 291 . 2 (𝜑 ↔ (⊤ ∧ 𝜑))
32bicomi 127 1 ((⊤ ∧ 𝜑) ↔ 𝜑)
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  wtru 1260
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-tru 1262
This theorem is referenced by:  truanfal  1309  truxortru  1326  truxorfal  1327
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