Theorem ancrd 324

Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)

Hypothesis

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

Assertion

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

Proof of Theorem ancrd

Step	Hyp	Ref	Expression
1		ancrd.1	. 2 |- ( ph -> ( ps -> ch ) )
2		idd 21	. 2 |- ( ph -> ( ps -> ps ) )
3	1, 2	jcad 305	1 |- ( ph -> ( ps -> ( ch /\ ps ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107

This theorem is referenced by:  impac  378  euan  2055  reupick  3360  prel12  3698  ssrnres  4981  funmo  5138  funssres  5165  dffo4  5568  dffo5  5569  fzospliti  9953  rexuz3  10762  qredeq  11777  prmdvdsfz  11819