Theorem aistia 38484

Description: Given a is equivalent to T., there exists a proof for a. (Contributed by Jarvin Udandy, 30-Aug-2016.)

Hypothesis

Ref	Expression
aistia.1	|- ( ph <-> T. )

Assertion

Ref	Expression
aistia	|- ph

Proof of Theorem aistia

Step	Hyp	Ref	Expression
1		aistia.1	. 2 |- ( ph <-> T. )
2		tbtru 1454	. 2 |- ( ph <-> ( ph <-> T. ) )
3	1, 2	mpbir 213	1 |- ph

Syntax hints:   <-> wb 188   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-tru 1447

This theorem is referenced by:  astbstanbst  38496  aistbistaandb  38497  aistbisfiaxb  38507  aisfbistiaxb  38508  aifftbifffaibif  38509  aifftbifffaibifff  38510  dandysum2p2e4  38586