Theorem adantld 276

Description: Deduction adding a conjunct to the left of an antecedent. (Contributed by NM, 4-May-1994.) (Proof shortened by Wolf Lammen, 20-Dec-2012.)

Hypothesis

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

Assertion

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

Proof of Theorem adantld

Step	Hyp	Ref	Expression
1		simpr 109	. 2 |- ( ( th /\ ps ) -> ps )
2		adantld.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	syl5 32	1 |- ( ph -> ( ( th /\ ps ) -> ch ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106

This theorem is referenced by:  jaoa  709  dedlema  953  dedlemb  954  prlem1  957  equveli  1732  poxp  6122  nnmordi  6405  eroprf  6515  xpdom2  6718  elni2  7115  prarloclemlo  7295  xrlttr  9574  fzen  9816  eluzgtdifelfzo  9967  ssfzo12bi  9995  climuni  11055  mulcn2  11074  serf0  11114  ntrivcvgap  11310  dfgcd2  11691  lcmgcdlem  11747  lcmdvds  11749  qnumdencl  11854  cnplimcim  12794  dveflem  12844