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  379  euan  2070  reupick  3406  prel12  3751  ssrnres  5046  funmo  5203  funssres  5230  dffo4  5633  dffo5  5634  fzospliti  10111  rexuz3  10932  qredeq  12028  prmdvdsfz  12071