Theorem pm3.34

Description: Theorem *3.34 (Syll) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.34	⊢ ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜑 → 𝜓 ) ) → ( 𝜑 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		imim2	⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) )
2	1	imp	⊢ ( ( ( 𝜓 → 𝜒 ) ∧ ( 𝜑 → 𝜓 ) ) → ( 𝜑 → 𝜒 ) )