Theorem anc2ri 581

Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)

Hypothesis

Ref	Expression
anc2ri.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
anc2ri	|- ( ph -> ( ps -> ( ch /\ ph ) ) )

Proof of Theorem anc2ri

Step	Hyp	Ref	Expression
1		anc2ri.1	. 2 |- ( ph -> ( ps -> ch ) )
2		id 22	. 2 |- ( ph -> ph )
3	1, 2	jctird 567	1 |- ( ph -> ( ps -> ( ch /\ ph ) ) )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  equvini  2346  fv3  6206  bropopvvv  7255  bropfvvvvlem  7256  issiga  30174  ontopbas  32427  bj-gl4lem  32579  clsk1independent  38344