Theorem jctl 290

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 8	. 2 |- (ph -> ps)
3		id 59	. 2 |- (ph -> ph)
4	2, 3	jca 288	1 |- (ph -> (ps /\ ph))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  equvini 1164  rabab 1813  vss 2297  relop 3265  odi 4194  oaabs 4236  mnfltt 5516  climge0 7049  pjpj0 9170  ococint 9212  cmbr4 9461

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain