Theorem ancrd 326

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 307	1 |- ( ph -> ( ps -> ( ch /\ ps ) ) )

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:  impac  381  euan  2134  reupick  3488  prel12  3849  ssrelrn  4914  ssrnres  5171  funmo  5333  funssres  5360  dffo4  5785  dffo5  5786  en2prde  7377  fzospliti  10386  rexuz3  11516  qredeq  12633  prmdvdsfz  12676