Theorem jctr 311

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 309	1 |- ( ph -> ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 107

This theorem is referenced by:  mpanl2  429  mpanr2  432  bm1.1  2085  undifss  3390  brprcneu  5346  mpoeq12  5763  tfri3  6194  ige2m2fzo  9816