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 )