Theorem 3ad2antr1 1189

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 1185	1 |- ( ( ph /\ ( ch /\ ps /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  ispod  4407  poxp  6406  fzosubel2  10486  hashdifpr  11130  pfxccat3a  11368  grpsubadd  13734  mulgnnass  13807  mulgnn0ass  13808  issubg2m  13839  srgdilem  14046  lsssn0  14449  dvconst  15488  dvconstre  15490  isclwwlk  16318  clwwlkccatlem  16324  clwwlkccat  16325