Metamath Proof Explorer


Theorem imbitrrid

Description: A mixed syllogism inference. (Contributed by NM, 3-Apr-1994)

Ref Expression
Hypotheses imbitrrid.1
|- ( ph -> th )
imbitrrid.2
|- ( ch -> ( ps <-> th ) )
Assertion imbitrrid
|- ( ch -> ( ph -> ps ) )

Proof

Step Hyp Ref Expression
1 imbitrrid.1
 |-  ( ph -> th )
2 imbitrrid.2
 |-  ( ch -> ( ps <-> th ) )
3 2 bicomd
 |-  ( ch -> ( th <-> ps ) )
4 1 3 imbitrid
 |-  ( ch -> ( ph -> ps ) )