Metamath Proof Explorer


Theorem a1dd

Description: Double deduction introducing an antecedent. Deduction associated with a1d . Double deduction associated with ax-1 and a1i . (Contributed by NM, 17-Dec-2004) (Proof shortened by Mel L. O'Cat, 15-Jan-2008)

Ref Expression
Hypothesis a1dd.1
|- ( ph -> ( ps -> ch ) )
Assertion a1dd
|- ( ph -> ( ps -> ( th -> ch ) ) )

Proof

Step Hyp Ref Expression
1 a1dd.1
 |-  ( ph -> ( ps -> ch ) )
2 ax-1
 |-  ( ch -> ( th -> ch ) )
3 1 2 syl6
 |-  ( ph -> ( ps -> ( th -> ch ) ) )