Theorem aistbistaandb 41077

Description: Given a is equivalent to T., also given that b is equivalent to T, there exists a proof for (a and b). (Contributed by Jarvin Udandy, 9-Sep-2016.)

Hypotheses

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

Assertion

Ref	Expression
aistbistaandb	|- ( ph /\ ps )

Proof of Theorem aistbistaandb

Step	Hyp	Ref	Expression
1		aistbistaandb.1	. . 3 |- ( ph <-> T. )
2	1	aistia 41064	. 2 |- ph
3		aistbistaandb.2	. . 3 |- ( ps <-> T. )
4	3	aistia 41064	. 2 |- ps
5	2, 4	pm3.2i 471	1 |- ( ph /\ ps )

Syntax hints:   <-> wb 196   /\ wa 384   T. wtru 1484

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 197  df-an 386  df-tru 1486

This theorem is referenced by: (None)