Metamath Proof Explorer


Theorem mpbii

Description: An inference from a nested biconditional, related to modus ponens. (Contributed by NM, 16-May-1993) (Proof shortened by Wolf Lammen, 25-Oct-2012)

Ref Expression
Hypotheses mpbii.min
|- ps
mpbii.maj
|- ( ph -> ( ps <-> ch ) )
Assertion mpbii
|- ( ph -> ch )

Proof

Step Hyp Ref Expression
1 mpbii.min
 |-  ps
2 mpbii.maj
 |-  ( ph -> ( ps <-> ch ) )
3 1 a1i
 |-  ( ph -> ps )
4 3 2 mpbid
 |-  ( ph -> ch )