Theorem wl-syl6 32430

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. Copy of syl6 34 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
wl-syl6.1	⊢ (𝜑 → (𝜓 → 𝜒))
wl-syl6.2	⊢ (𝜒 → 𝜃)

Assertion

Ref	Expression
wl-syl6	⊢ (𝜑 → (𝜓 → 𝜃))

Proof of Theorem wl-syl6

Step	Hyp	Ref	Expression
1		wl-syl6.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		wl-syl6.2	. . 3 ⊢ (𝜒 → 𝜃)
3	2	wl-imim2i 32429	. 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → 𝜃))
4	1, 3	wl-syl 32422	1 ⊢ (𝜑 → (𝜓 → 𝜃))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 32417  ax-luk2 32418  ax-luk3 32419

This theorem is referenced by:  wl-ax3  32431  wl-pm2.27  32433