Theorem impel 280

Description: An inference for implication elimination. (Contributed by Giovanni Mascellani, 23-May-2019.) (Proof shortened by Wolf Lammen, 2-Sep-2020.)

Hypotheses

Ref	Expression
impel.1	|- ( ph -> ( ps -> ch ) )
impel.2	|- ( th -> ps )

Assertion

Ref	Expression
impel	|- ( ( ph /\ th ) -> ch )

Proof of Theorem impel

Step	Hyp	Ref	Expression
1		impel.2	. . 3 |- ( th -> ps )
2		impel.1	. . 3 |- ( ph -> ( ps -> ch ) )
3	1, 2	syl5 32	. 2 |- ( ph -> ( th -> ch ) )
4	3	imp 124	1 |- ( ( ph /\ th ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem is referenced by:  pm4.55dc  944  fiintim  7093  eqinfti  7187  finomni  7307  frecuzrdgrclt  10637  seq3coll  11064  swrdswrd  11237  swrdccatin1  11257  swrdccatin2  11261  fprodsplitsn  12144  nninfctlemfo  12561  unct  13013  isnzr2  14148  dvcnp2cntop  15373  fsumdvdsmul  15665  perfectlem2  15674  upgrwlkcompim  16073  wlkv0  16080