This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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 ) ) )