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  3466  difsn  3759  preq12b  3800  elres  4982  relssres  4984  fnoprabg  6023  1idprl  7657  1idpru  7658  msqge0  8643  mulge0  8646  fzospliti  10252  algcvga  12219  prmind2  12288  sqrt2irr  12330  grpinveu  13170  metrest  14742  2sqlem10  15366