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	$$⊢\phi \leftrightarrow \top$$
	astbstanbst.2	$$⊢\psi \leftrightarrow \top$$
Assertion	astbstanbst	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \top$$

Proof

Step	Hyp	Ref	Expression
1		astbstanbst.1	$$⊢\phi \leftrightarrow \top$$
2		astbstanbst.2	$$⊢\psi \leftrightarrow \top$$
3	1	aistia	$$⊢\phi$$
4	2	aistia	$$⊢\psi$$
5	3 4	pm3.2i	$$⊢\left(\phi \wedge \psi \right)$$
6	5	bitru	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \top$$