Theorem 3bior1fand 1439

Description: A disjunction is equivalent to a threefold disjunction with single falsehood of a conjunction. (Contributed by Alexander van der Vekens, 8-Sep-2017.)

Hypothesis

Ref	Expression
3biorfd.1	|- ( ph -> -. th )

Assertion

Ref	Expression
3bior1fand	|- ( ph -> ( ( ch \/ ps ) <-> ( ( th /\ ta ) \/ ch \/ ps ) ) )

Proof of Theorem 3bior1fand

Step	Hyp	Ref	Expression
1		3biorfd.1	. . 3 |- ( ph -> -. th )
2	1	intnanrd 963	. 2 |- ( ph -> -. ( th /\ ta ) )
3	2	3bior1fd 1438	1 |- ( ph -> ( ( ch \/ ps ) <-> ( ( th /\ ta ) \/ ch \/ ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384   \/ w3o 1036

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-3or 1038

This theorem is referenced by: (None)