Theorem jctl 312

Description: Inference conjoining a theorem to the left of a consequent. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 24-Oct-2012.)

Hypothesis

Ref	Expression
jctl.1	|- ps

Assertion

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

Proof of Theorem jctl

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ph -> ph )
2		jctl.1	. 2 |- ps
3	1, 2	jctil 310	1 |- ( ph -> ( ps /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 103

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

This theorem is referenced by:  mpanl1  432  mpanlr1  438  reg2exmidlema  4518  relop  4761  nn0n0n1ge2  9282  expge1  10513  4dvdseven  11876  ndvdsp1  11891