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Metamath Proof Explorer

Theorem truan

Description: True can be removed from a conjunction. (Contributed by FL, 20-Mar-2011) (Proof shortened by Wolf Lammen, 21-Jul-2019)

Ref Expression
Assertion truan ( ( ⊤ ∧ 𝜑 ) ↔ 𝜑 )

Proof

Step Hyp Ref Expression
1 tru ⊢ ⊤
2 1 biantrur ⊢ ( 𝜑 ↔ ( ⊤ ∧ 𝜑 ) )
3 2 bicomi ⊢ ( ( ⊤ ∧ 𝜑 ) ↔ 𝜑 )