Theorem adantld 278

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 110	. 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 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107

This theorem is referenced by:  jaoa  720  dedlema  969  dedlemb  970  prlem1  973  equveli  1759  poxp  6236  nnmordi  6520  eroprf  6631  xpdom2  6834  elni2  7316  prarloclemlo  7496  xrlttr  9798  fzen  10046  eluzgtdifelfzo  10200  ssfzo12bi  10228  climuni  11304  mulcn2  11323  serf0  11363  ntrivcvgap  11559  dfgcd2  12018  lcmgcdlem  12080  lcmdvds  12082  qnumdencl  12190  infpnlem1  12360  cnplimcim  14276  dveflem  14327  bj-charfundcALT  14701