Theorem tradd

Description: Add top ad a conjunct. (Contributed by Giovanni Mascellani, 24-May-2019)

	Ref	Expression
Hypothesis	tradd.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	tradd	⊢ ( 𝜑 ↔ ( ⊤ ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		tradd.1	⊢ ( 𝜑 ↔ 𝜓 )
2		truan	⊢ ( ( ⊤ ∧ 𝜓 ) ↔ 𝜓 )
3	1 2	bitr4i	⊢ ( 𝜑 ↔ ( ⊤ ∧ 𝜓 ) )