Metamath Proof Explorer


Theorem 2a1dd

Description: Double deduction introducing two antecedents. Two applications of 2a1dd . Deduction associated with 2a1d . Double deduction associated with 2a1 and 2a1i . (Contributed by Jeff Hankins, 5-Aug-2009)

Ref Expression
Hypothesis 2a1dd.1
|- ( ph -> ( ps -> ch ) )
Assertion 2a1dd
|- ( ph -> ( ps -> ( th -> ( ta -> ch ) ) ) )

Proof

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