Theorem wl-mps

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

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

Proof

Step	Hyp	Ref	Expression
1		wl-mps.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		wl-mps.2	⊢ ( ( 𝜑 → 𝜒 ) → 𝜃 )
3	1	a2i	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) )
4	3 2	syl	⊢ ( ( 𝜑 → 𝜓 ) → 𝜃 )