Theorem pm3.33

Description: Theorem *3.33 (Syll) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.33	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜓 → 𝜒 ) ) → ( 𝜑 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		imim1	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) ) )
2	1	imp	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜓 → 𝜒 ) ) → ( 𝜑 → 𝜒 ) )