Theorem ancld 325

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

Hypothesis

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

Assertion

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

Proof of Theorem ancld

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( ps -> ps ) )
2		ancld.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	jcad 307	1 |- ( ph -> ( ps -> ( ps /\ ch ) ) )

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:  mopick2  2128  cgsexg  2798  cgsex2g  2799  cgsex4g  2800  reximdva0m  3467  difsn  3760  preq12b  3801  elres  4983  relssres  4985  fnoprabg  6024  1idprl  7659  1idpru  7660  msqge0  8645  mulge0  8648  fzospliti  10254  algcvga  12229  prmind2  12298  sqrt2irr  12340  grpinveu  13180  metrest  14752  2sqlem10  15376