Theorem tradd

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

	Ref	Expression
Hypothesis	tradd.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	tradd	$$⊢\phi \leftrightarrow \left(\top \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		tradd.1	$$⊢\phi \leftrightarrow \psi$$
2		truan	$$⊢\left(\top \wedge \psi \right)\leftrightarrow \psi$$
3	1 2	bitr4i	$$⊢\phi \leftrightarrow \left(\top \wedge \psi \right)$$