Theorem adantrrl 760

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)

Hypothesis

Ref	Expression
adantr2.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

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

Proof of Theorem adantrrl

Step	Hyp	Ref	Expression
1		simpr 477	. 2 |- ( ( ta /\ ch ) -> ch )
2		adantr2.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylanr2 685	1 |- ( ( ph /\ ( ps /\ ( ta /\ ch ) ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  1stconst  7265  zorn2lem6  9323  ltmul12a  10879  mrcmndind  17366  neiint  20908  neissex  20931  1stcfb  21248  1stcrest  21256  grporcan  27372  mdslmd3i  29191  colineardim1  32168  cvratlem  34707  ps-2  34764