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  947  mapsnd  6925  fiintim  7193  eqinfti  7313  finomni  7433  frecuzrdgrclt  10781  seq3coll  11218  swrdswrd  11401  swrdccatin1  11421  swrdccatin2  11425  fprodsplitsn  12323  nninfctlemfo  12740  unct  13210  isnzr2  14346  dvcnp2cntop  15581  fsumdvdsmul  15876  perfectlem2  15885  upgrwlkcompim  16374  wlkv0  16381  trlsegvdeglem1  16472