Theorem jctl 238

Description: Inference conjoining a theorem to the left of a consequent.

Hypothesis

Ref	Expression
jctl.1	|- ps

Assertion

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

Proof of Theorem jctl

Step	Hyp	Ref	Expression
1		jctl.1	. . 3 |- ps
2	1	a1i 7	. 2 |- (ph -> ps)
3		id 9	. 2 |- (ph -> ph)
4	2, 3	jca 236	1 |- (ph -> (ps /\ ph))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  eqvin.l1 851  rabab 1359  vss 1729  recdivt 4270  pjpj0 5259  ococint 5298  shunss 5338  cmbr4 5510

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org