Metamath Proof Explorer


Theorem syl3an12

Description: A double syllogism inference. (Contributed by SN, 15-Sep-2024)

Ref Expression
Hypotheses syl3an12.1 φ ψ
syl3an12.2 χ θ
syl3an12.s ψ θ τ η
Assertion syl3an12 φ χ τ η

Proof

Step Hyp Ref Expression
1 syl3an12.1 φ ψ
2 syl3an12.2 χ θ
3 syl3an12.s ψ θ τ η
4 id τ τ
5 1 2 4 3 syl3an φ χ τ η