Theorem 3adantr3 1182

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Hypothesis

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

Assertion

Ref	Expression
3adantr3	|- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )

Proof of Theorem 3adantr3

Step	Hyp	Ref	Expression
1		3simpa 1018	. 2 |- ( ( ps /\ ch /\ ta ) -> ( ps /\ ch ) )
2		3adantr.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylan2 286	1 |- ( ( ph /\ ( ps /\ ch /\ 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:  3ad2antr1  1186  3ad2antr2  1187  3adant3r3  1238  isosolem  5947  caovlem2d  6197  swrdspsleq  11194  tanaddap  12245  prdssgrpd  13443  prdsmndd  13476  mhmmnd  13648  imasrng  13914  imasring  14022  isxmet2d  15016  xmetres2  15047  comet  15167  xmetxp  15175  iswlkg  16032