Theorem jca

Description: Deduce conjunction of the consequents of two implications ("join consequents with 'and'"). Deduction form of pm3.2 and pm3.2i . Its associated deduction is jcad . Equivalent to the natural deduction rule /\ I ( /\ introduction), see natded . (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 25-Oct-2012)

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

Proof

Step	Hyp	Ref	Expression
1		jca.1	|- ( ph -> ps )
2		jca.2	|- ( ph -> ch )
3		pm3.2	|- ( ps -> ( ch -> ( ps /\ ch ) ) )
4	1 2 3	sylc	|- ( ph -> ( ps /\ ch ) )