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Theorem tradd 33077
Description: Add top ad a conjunct. (Contributed by Giovanni Mascellani, 24-May-2019.)
Hypothesis
Ref Expression
tradd.1 (𝜑𝜓)
Assertion
Ref Expression
tradd (𝜑 ↔ (⊤ ∧ 𝜓))

Proof of Theorem tradd
StepHypRef Expression
1 tradd.1 . 2 (𝜑𝜓)
2 truan 1492 . 2 ((⊤ ∧ 𝜓) ↔ 𝜓)
31, 2bitr4i 266 1 (𝜑 ↔ (⊤ ∧ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 195  wa 383  wtru 1476
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 196  df-an 385  df-tru 1478
This theorem is referenced by: (None)
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