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Metamath Proof Explorer

Theorem 3syl

Description: Inference chaining two syllogisms syl . Inference associated with imim12i . (Contributed by NM, 28-Dec-1992)

Ref Expression
Hypotheses 3syl.1 
|- ( ph -> ps )
3syl.2 
|- ( ps -> ch )
3syl.3 
|- ( ch -> th )
Assertion 3syl 
|- ( ph -> th )

Proof

Step Hyp Ref Expression
1 3syl.1 
 |-  ( ph -> ps )
2 3syl.2 
 |-  ( ps -> ch )
3 3syl.3 
 |-  ( ch -> th )
4 1 2 syl 
 |-  ( ph -> ch )
5 4 3 syl 
 |-  ( ph -> th )