Theorem 3adantr3 1184

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 1020	. 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 1004

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 1006

This theorem is referenced by:  3ad2antr1  1188  3ad2antr2  1189  3adant3r3  1240  isosolem  5964  caovlem2d  6214  swrdspsleq  11247  tanaddap  12299  prdssgrpd  13497  prdsmndd  13530  mhmmnd  13702  imasrng  13968  imasring  14076  isxmet2d  15071  xmetres2  15102  comet  15222  xmetxp  15230  iswlkg  16179