Theorem aisfina 41065

Description: Given a is equivalent to F., there exists a proof for not a. (Contributed by Jarvin Udandy, 30-Aug-2016.)

Hypothesis

Ref	Expression
aisfina.1	|- ( ph <-> F. )

Assertion

Ref	Expression
aisfina	|- -. ph

Proof of Theorem aisfina

Step	Hyp	Ref	Expression
1		aisfina.1	. 2 |- ( ph <-> F. )
2		nbfal 1495	. 2 |- ( -. ph <-> ( ph <-> F. ) )
3	1, 2	mpbir 221	1 |- -. ph

Syntax hints:   -. wn 3   <-> wb 196   F. wfal 1488

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-tru 1486  df-fal 1489

This theorem is referenced by:  aistbisfiaxb  41086  aisfbistiaxb  41087  aifftbifffaibif  41088  aifftbifffaibifff  41089  atnaiana  41090  dandysum2p2e4  41165