Theorem 3adantr3 1189

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 1025	. 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 )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  3ad2antr1  1193  3ad2antr2  1194  3adant3r3  1245  isosolem  6030  caovlem2d  6282  swrdspsleq  11453  tanaddap  12522  mhmmnd  13968  prdssgrpd  14240  prdsmndd  14243  imasrng  14304  imasring  14418  isxmet2d  15498  xmetres2  15529  comet  15649  xmetxp  15657  iswlkg  16668