Theorem aistia 38241

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 1448	. 2 |- ( ph <-> ( ph <-> T. ) )
3	1, 2	mpbir 213	1 |- ph

Syntax hints:   <-> wb 188   T. wtru 1439

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 1441

This theorem is referenced by:  astbstanbst  38253  aistbistaandb  38254  aistbisfiaxb  38264  aisfbistiaxb  38265  aifftbifffaibif  38266  aifftbifffaibifff  38267  dandysum2p2e4  38343