Theorem 3ad2antr1 1164

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 1160	1 |- ( ( ph /\ ( ch /\ ps /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  ispod  4336  poxp  6287  fzosubel2  10265  hashdifpr  10894  grpsubadd  13163  mulgnnass  13230  mulgnn0ass  13231  issubg2m  13262  srgdilem  13468  lsssn0  13869  dvconst  14873  dvconstre  14875