Theorem astbstanbst 38496

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.)

Hypotheses

Ref	Expression
astbstanbst.1	|- ( ph <-> T. )
astbstanbst.2	|- ( ps <-> T. )

Assertion

Ref	Expression
astbstanbst	|- ( ( ph /\ ps ) <-> T. )

Proof of Theorem astbstanbst

Step	Hyp	Ref	Expression
1		astbstanbst.1	. . . 4 |- ( ph <-> T. )
2	1	aistia 38484	. . 3 |- ph
3		astbstanbst.2	. . . 4 |- ( ps <-> T. )
4	3	aistia 38484	. . 3 |- ps
5	2, 4	pm3.2i 457	. 2 |- ( ph /\ ps )
6	5	bitru 1456	1 |- ( ( ph /\ ps ) <-> T. )

Syntax hints:   <-> wb 188   /\ wa 371   T. wtru 1445

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447

This theorem is referenced by:  dandysum2p2e4  38586