Theorem atnaiana 41090

Description: Given a, it is not the case a implies a self contradiction. (Contributed by Jarvin Udandy, 7-Sep-2020.)

Hypothesis

Ref	Expression
atnaiana.1	|- ph

Assertion

Ref	Expression
atnaiana	|- -. ( ph -> ( ph /\ -. ph ) )

Proof of Theorem atnaiana

Step	Hyp	Ref	Expression
1		atnaiana.1	. . . 4 |- ph
2	1	bitru 1496	. . 3 |- ( ph <-> T. )
3		pm3.24 926	. . . 4 |- -. ( ph /\ -. ph )
4	3	bifal 1497	. . 3 |- ( ( ph /\ -. ph ) <-> F. )
5	2, 4	aifftbifffaibif 41088	. 2 |- ( ( ph -> ( ph /\ -. ph ) ) <-> F. )
6	5	aisfina 41065	1 |- -. ( ph -> ( ph /\ -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384

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  df-fal 1489

This theorem is referenced by:  ainaiaandna  41091  confun5  41110