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Theorem truan 1259
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 1246 . . 3
21biantrur 287 . 2 (φ ↔ ( ⊤ φ))
32bicomi 123 1 (( ⊤ φ) ↔ φ)
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wtru 1243
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-tru 1245
This theorem is referenced by:  truanfal  1290  truxortru  1307  truxorfal  1308
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