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 ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  impac  381  euan  2143  reupick  3517  prel12  3896  ssrelrn  4972  ssrnres  5230  funmo  5392  funssres  5420  dffo4  5856  dffo5  5857  en2prde  7539  fzospliti  10585  rexuz3  11756  qredeq  12874  prmdvdsfz  12917