Theorem ifpnim2 37844

Description: Restate negated implication as conditional logic operator. (Contributed by RP, 25-Apr-2020.)

Assertion

Ref	Expression
ifpnim2	|- ( -. ( ph -> ps ) <-> if- ( ps , -. ps , ph ) )

Proof of Theorem ifpnim2

Step	Hyp	Ref	Expression
1		ifpnot23c 37829	. 2 |- ( -. if- ( ps , ps , -. ph ) <-> if- ( ps , -. ps , ph ) )
2		ifpim4 37843	. 2 |- ( ( ph -> ps ) <-> if- ( ps , ps , -. ph ) )
3	1, 2	xchnxbir 323	1 |- ( -. ( ph -> ps ) <-> if- ( ps , -. ps , ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196  if-wif 1012

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-or 385  df-an 386  df-ifp 1013

This theorem is referenced by: (None)