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  2137  cgsexg  2807  cgsex2g  2808  cgsex4g  2809  reximdva0m  3476  difsn  3770  preq12b  3811  elres  4996  relssres  4998  fnoprabg  6048  1idprl  7705  1idpru  7706  msqge0  8691  mulge0  8694  fzospliti  10302  algcvga  12406  prmind2  12475  sqrt2irr  12517  grpinveu  13403  metrest  15011  2sqlem10  15635