Theorem jctr 315

Description: Inference conjoining a theorem to the right of a consequent. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 24-Oct-2012.)

Hypothesis

Ref	Expression
jctl.1	|- ps

Assertion

Ref	Expression
jctr	|- ( ph -> ( ph /\ ps ) )

Proof of Theorem jctr

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ph -> ph )
2		jctl.1	. 2 |- ps
3	1, 2	jctir 313	1 |- ( ph -> ( ph /\ ps ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  mpanl2  439  mpanr2  442  bm1.1  2223  undifss  3608  brprcneu  5688  mpoeq12  6148  tfri3  6638  ige2m2fzo  10616  konigsbergssiedgwpren  16726