Metamath Proof Explorer

Theorem astbstanbst

Description: Given a is equivalent to T., also given that b is equivalent to T, there exists a proof for a and b is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016)

	Ref	Expression
Hypotheses	astbstanbst.1	$⊢ φ \leftrightarrow ⊤$
	astbstanbst.2	$⊢ ψ \leftrightarrow ⊤$
Assertion	astbstanbst	$⊢ (φ \land ψ) \leftrightarrow ⊤$

Proof

Step	Hyp	Ref	Expression
1		astbstanbst.1	$⊢ φ \leftrightarrow ⊤$
2		astbstanbst.2	$⊢ ψ \leftrightarrow ⊤$
3	1	aistia	$⊢ φ$
4	2	aistia	$⊢ ψ$
5	3 4	pm3.2i	$⊢ (φ \land ψ)$
6	5	bitru	$⊢ (φ \land ψ) \leftrightarrow ⊤$