Theorem wl-syls2

Description: Replacing a nested antecedent. A sort of syllogism in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	wl-syls2.1	⊢ ( 𝜑 → 𝜓 )
	wl-syls2.2	⊢ ( ( 𝜑 → 𝜒 ) → 𝜃 )
Assertion	wl-syls2	⊢ ( ( 𝜓 → 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		wl-syls2.1	⊢ ( 𝜑 → 𝜓 )
2		wl-syls2.2	⊢ ( ( 𝜑 → 𝜒 ) → 𝜃 )
3	1	imim1i	⊢ ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) )
4	3 2	syl	⊢ ( ( 𝜓 → 𝜒 ) → 𝜃 )