Theorem jctir 313

Description: Inference conjoining a theorem to right of consequent in an implication. (Contributed by NM, 31-Dec-1993.)

Hypotheses

Ref	Expression
jctil.1	|- ( ph -> ps )
jctil.2	|- ch

Assertion

Ref	Expression
jctir	|- ( ph -> ( ps /\ ch ) )

Proof of Theorem jctir

Step	Hyp	Ref	Expression
1		jctil.1	. 2 |- ( ph -> ps )
2		jctil.2	. . 3 |- ch
3	2	a1i 9	. 2 |- ( ph -> ch )
4	1, 3	jca 306	1 |- ( ph -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  jctr  315  equvini  1758  funtp  5270  foimacnv  5480  respreima  5645  fpr  5699  dmtpos  6257  ixpsnf1o  6736  ssdomg  6778  exmidfodomrlemim  7200  archnqq  7416  recexgt0sr  7772  ige2m2fzo  10198  climeu  11304  algcvgblem  12049  qredeu  12097  qnumdencoprm  12193  qeqnumdivden  12194  eltg3i  13559  topbas  13570  neipsm  13657  lmbrf  13718  exmidsbthrlem  14773