Theorem jctir 296

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 290	1 |- ( ph -> ( ps /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101

This theorem is referenced by:  jctr  298  equvini  1641  funtp  4952  foimacnv  5144  respreima  5295  fpr  5345  dmtpos  5871  ssdomg  6258  archnqq  6515  recexgt0sr  6858  ige2m2fzo  9054  climeu  9817  algcvgblem  9888