Theorem jctl 314

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 312	1 |- ( ph -> ( ps /\ ph ) )

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:  mpanl1  438  mpanlr1  444  reg2exmidlema  4681  relop  4930  nn0n0n1ge2  9715  expge1  11013  swrdccatin2  11501  4dvdseven  12684  ndvdsp1  12699