Theorem 3orim123da

Description: Disjoin antecedents and consequents of three premises. (Contributed by Thierry Arnoux, 13-Jul-2026)

	Ref	Expression
Hypotheses	3orim123da.1	|- ( ph -> ( ps \/ th \/ et ) )
	3orim123da.2	|- ( ( ph /\ ps ) -> ch )
	3orim123da.3	|- ( ( ph /\ th ) -> ta )
	3orim123da.4	|- ( ( ph /\ et ) -> ze )
Assertion	3orim123da	|- ( ph -> ( ch \/ ta \/ ze ) )

Proof

Step	Hyp	Ref	Expression
1		3orim123da.1	|- ( ph -> ( ps \/ th \/ et ) )
2		3orim123da.2	|- ( ( ph /\ ps ) -> ch )
3		3orim123da.3	|- ( ( ph /\ th ) -> ta )
4		3orim123da.4	|- ( ( ph /\ et ) -> ze )
5	2	ex	|- ( ph -> ( ps -> ch ) )
6	3	ex	|- ( ph -> ( th -> ta ) )
7	4	ex	|- ( ph -> ( et -> ze ) )
8	5 6 7	3orim123d	|- ( ph -> ( ( ps \/ th \/ et ) -> ( ch \/ ta \/ ze ) ) )
9	1 8	mpd	|- ( ph -> ( ch \/ ta \/ ze ) )