Theorem orim12d

Description: Disjoin antecedents and consequents in a deduction. See orim12dALT for a proof which does not depend on df-an . (Contributed by NM, 10-May-1994)

	Ref	Expression
Hypotheses	orim12d.1	|- ( ph -> ( ps -> ch ) )
	orim12d.2	|- ( ph -> ( th -> ta ) )
Assertion	orim12d	|- ( ph -> ( ( ps \/ th ) -> ( ch \/ ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		orim12d.1	|- ( ph -> ( ps -> ch ) )
2		orim12d.2	|- ( ph -> ( th -> ta ) )
3		pm3.48	|- ( ( ( ps -> ch ) /\ ( th -> ta ) ) -> ( ( ps \/ th ) -> ( ch \/ ta ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( ( ps \/ th ) -> ( ch \/ ta ) ) )