Theorem confun2 41107

Description: Confun simplified to two propositions. (Contributed by Jarvin Udandy, 6-Sep-2020.)

Hypotheses

Ref	Expression
confun2.1	|- ( ps -> ph )
confun2.2	|- ( ps -> -. ( ps -> ( ps /\ -. ps ) ) )
confun2.3	|- ( ( ps -> ph ) -> ( ( ps -> ph ) -> ph ) )

Assertion

Ref	Expression
confun2	|- ( ps -> ( -. ( ps -> ( ps /\ -. ps ) ) <-> ( ps -> ph ) ) )

Proof of Theorem confun2

Step	Hyp	Ref	Expression
1		confun2.1	. 2 |- ( ps -> ph )
2		confun2.2	. 2 |- ( ps -> -. ( ps -> ( ps /\ -. ps ) ) )
3		confun2.3	. 2 |- ( ( ps -> ph ) -> ( ( ps -> ph ) -> ph ) )
4	1, 1, 2, 3	confun 41106	1 |- ( ps -> ( -. ( ps -> ( ps /\ -. ps ) ) <-> ( ps -> ph ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ 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

This theorem is referenced by: (None)