Theorem confun3 38539

Description: Confun's more complex form where both a,d have been "defined". (Contributed by Jarvin Udandy, 6-Sep-2020.)

Hypotheses

Ref	Expression
confun3.1	|- ( ph <-> ( ch -> ps ) )
confun3.2	|- ( th <-> -. ( ch -> ( ch /\ -. ch ) ) )
confun3.3	|- ( ch -> ps )
confun3.4	|- ( ch -> -. ( ch -> ( ch /\ -. ch ) ) )
confun3.5	|- ( ( ch -> ps ) -> ( ( ch -> ps ) -> ps ) )

Assertion

Ref	Expression
confun3	|- ( ch -> ( -. ( ch -> ( ch /\ -. ch ) ) <-> ( ch -> ps ) ) )

Proof of Theorem confun3

Step	Hyp	Ref	Expression
1		confun3.3	. 2 |- ( ch -> ps )
2		confun3.4	. 2 |- ( ch -> -. ( ch -> ( ch /\ -. ch ) ) )
3		confun3.5	. 2 |- ( ( ch -> ps ) -> ( ( ch -> ps ) -> ps ) )
4	1, 1, 2, 3	confun 38537	1 |- ( ch -> ( -. ( ch -> ( ch /\ -. ch ) ) <-> ( ch -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 188   /\ wa 371

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

This theorem is referenced by: (None)