Theorem 3adantr3 1160

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 996	. 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 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:  3ad2antr1  1164  3ad2antr2  1165  3adant3r3  1216  isosolem  5892  caovlem2d  6138  tanaddap  12021  prdssgrpd  13218  prdsmndd  13251  mhmmnd  13423  imasrng  13689  imasring  13797  isxmet2d  14791  xmetres2  14822  comet  14942  xmetxp  14950