Metamath Proof Explorer


Theorem ifpnancor

Description: Corollary of commutation of and. (Contributed by RP, 25-Apr-2020)

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

Proof

Step Hyp Ref Expression
1 ifpancor
 |-  ( if- ( ph , ps , ph ) <-> if- ( ps , ph , ps ) )
2 1 notbii
 |-  ( -. if- ( ph , ps , ph ) <-> -. if- ( ps , ph , ps ) )
3 ifpnot23
 |-  ( -. if- ( ph , ps , ph ) <-> if- ( ph , -. ps , -. ph ) )
4 ifpnot23
 |-  ( -. if- ( ps , ph , ps ) <-> if- ( ps , -. ph , -. ps ) )
5 2 3 4 3bitr3i
 |-  ( if- ( ph , -. ps , -. ph ) <-> if- ( ps , -. ph , -. ps ) )