Theorem ifpan123g 37803

Description: Conjunction of conditional logical operators. (Contributed by RP, 18-Apr-2020.)

Assertion

Ref	Expression
ifpan123g	|- ( (if- ( ph , ch , ta ) /\ if- ( ps , th , et ) ) <-> ( ( ( -. ph \/ ch ) /\ ( ph \/ ta ) ) /\ ( ( -. ps \/ th ) /\ ( ps \/ et ) ) ) )

Proof of Theorem ifpan123g

Step	Hyp	Ref	Expression
1		dfifp4 1016	. 2 |- (if- ( ph , ch , ta ) <-> ( ( -. ph \/ ch ) /\ ( ph \/ ta ) ) )
2		dfifp4 1016	. 2 |- (if- ( ps , th , et ) <-> ( ( -. ps \/ th ) /\ ( ps \/ et ) ) )
3	1, 2	anbi12i 733	1 |- ( (if- ( ph , ch , ta ) /\ if- ( ps , th , et ) ) <-> ( ( ( -. ph \/ ch ) /\ ( ph \/ ta ) ) /\ ( ( -. ps \/ th ) /\ ( ps \/ et ) ) ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383   /\ wa 384  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:  ifpan23  37804