Metamath Proof Explorer


Theorem syl5d

Description: A nested syllogism deduction. Deduction associated with syl5 . (Contributed by NM, 14-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000) (Proof shortened by Mel L. O'Cat, 2-Feb-2006)

Ref Expression
Hypotheses syl5d.1 φ ψ χ
syl5d.2 φ θ χ τ
Assertion syl5d φ θ ψ τ

Proof

Step Hyp Ref Expression
1 syl5d.1 φ ψ χ
2 syl5d.2 φ θ χ τ
3 1 a1d φ θ ψ χ
4 3 2 syldd φ θ ψ τ