Metamath Proof Explorer


Theorem 3imp3i2an

Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 13-Apr-2022)

Ref Expression
Hypotheses 3imp3i2an.1 φ ψ χ θ
3imp3i2an.2 φ χ τ
3imp3i2an.3 θ τ η
Assertion 3imp3i2an φ ψ χ η

Proof

Step Hyp Ref Expression
1 3imp3i2an.1 φ ψ χ θ
2 3imp3i2an.2 φ χ τ
3 3imp3i2an.3 θ τ η
4 2 3adant2 φ ψ χ τ
5 1 4 3 syl2anc φ ψ χ η