Metamath Proof Explorer


Theorem syl5ibrcom

Description: A mixed syllogism inference. (Contributed by NM, 20-Jun-2007)

Ref Expression
Hypotheses imbitrrid.1
|- ( ph -> th )
imbitrrid.2
|- ( ch -> ( ps <-> th ) )
Assertion syl5ibrcom
|- ( ph -> ( ch -> ps ) )

Proof

Step Hyp Ref Expression
1 imbitrrid.1
 |-  ( ph -> th )
2 imbitrrid.2
 |-  ( ch -> ( ps <-> th ) )
3 1 2 imbitrrid
 |-  ( ch -> ( ph -> ps ) )
4 3 com12
 |-  ( ph -> ( ch -> ps ) )