Theorem 3ad2antr1 1186

Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 25-Dec-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antr1	|- ( ( ph /\ ( ch /\ ps /\ ta ) ) -> th )

Proof of Theorem 3ad2antr1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantrr 479	. 2 |- ( ( ph /\ ( ch /\ ps ) ) -> th )
3	2	3adantr3 1182	1 |- ( ( ph /\ ( ch /\ ps /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1004

This theorem is referenced by:  ispod  4395  poxp  6384  fzosubel2  10413  hashdifpr  11055  pfxccat3a  11286  grpsubadd  13637  mulgnnass  13710  mulgnn0ass  13711  issubg2m  13742  srgdilem  13948  lsssn0  14350  dvconst  15384  dvconstre  15386  isclwwlk  16137  clwwlkccatlem  16143  clwwlkccat  16144