Theorem ifpnotnotb 37824

Description: Factor conditional logic operator over negation in terms 2 and 3. (Contributed by RP, 21-Apr-2020.)

Assertion

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

Proof of Theorem ifpnotnotb

Step	Hyp	Ref	Expression
1		ifpnot23 37823	. 2 |- ( -. if- ( ph , ps , ch ) <-> if- ( ph , -. ps , -. ch ) )
2	1	bicomi 214	1 |- (if- ( ph , -. ps , -. ch ) <-> -. if- ( ph , ps , ch ) )

Syntax hints:   -. wn 3   <-> 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:  ifpananb  37851  ifpnannanb  37852  ifpxorxorb  37856