Metamath Proof Explorer


Theorem syl3an1b

Description: A syllogism inference. (Contributed by NM, 22-Aug-1995)

Ref Expression
Hypotheses syl3an1b.1 ( 𝜑𝜓 )
syl3an1b.2 ( ( 𝜓𝜒𝜃 ) → 𝜏 )
Assertion syl3an1b ( ( 𝜑𝜒𝜃 ) → 𝜏 )

Proof

Step Hyp Ref Expression
1 syl3an1b.1 ( 𝜑𝜓 )
2 syl3an1b.2 ( ( 𝜓𝜒𝜃 ) → 𝜏 )
3 1 biimpi ( 𝜑𝜓 )
4 3 2 syl3an1 ( ( 𝜑𝜒𝜃 ) → 𝜏 )