Theorem 3adantr3 1161

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 997	. 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 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:  3ad2antr1  1165  3ad2antr2  1166  3adant3r3  1217  isosolem  5893  caovlem2d  6139  swrdspsleq  11120  tanaddap  12050  prdssgrpd  13247  prdsmndd  13280  mhmmnd  13452  imasrng  13718  imasring  13826  isxmet2d  14820  xmetres2  14851  comet  14971  xmetxp  14979