Theorem 3ad2antr1 1165

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 1161	1 |- ( ( ph /\ ( ch /\ ps /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

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 983

This theorem is referenced by:  ispod  4351  poxp  6318  fzosubel2  10324  hashdifpr  10965  grpsubadd  13420  mulgnnass  13493  mulgnn0ass  13494  issubg2m  13525  srgdilem  13731  lsssn0  14132  dvconst  15166  dvconstre  15168