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  5269  foimacnv  5479  respreima  5644  fpr  5698  dmtpos  6256  ixpsnf1o  6735  ssdomg  6777  exmidfodomrlemim  7199  archnqq  7415  recexgt0sr  7771  ige2m2fzo  10197  climeu  11303  algcvgblem  12048  qredeu  12096  qnumdencoprm  12192  qeqnumdivden  12193  eltg3i  13526  topbas  13537  neipsm  13624  lmbrf  13685  exmidsbthrlem  14740