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	|- ( ph <-> T. )
	astbstanbst.2	|- ( ps <-> T. )
Assertion	astbstanbst	|- ( ( ph /\ ps ) <-> T. )

Proof

Step	Hyp	Ref	Expression
1		astbstanbst.1	|- ( ph <-> T. )
2		astbstanbst.2	|- ( ps <-> T. )
3	1	aistia	|- ph
4	2	aistia	|- ps
5	3 4	pm3.2i	|- ( ph /\ ps )
6	5	bitru	|- ( ( ph /\ ps ) <-> T. )