Theorem wl-syl 32422

Description: An inference version of the transitive laws for implication luk-1 1571. Copy of syl 17 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
wl-syl	⊢ (𝜑 → 𝜒)

Proof of Theorem wl-syl

Step	Hyp	Ref	Expression
1		wl-syl.2	. 2 ⊢ (𝜓 → 𝜒)
2		wl-syl.1	. . 3 ⊢ (𝜑 → 𝜓)
3	2	wl-imim1i 32421	. 2 ⊢ ((𝜓 → 𝜒) → (𝜑 → 𝜒))
4	1, 3	ax-mp 5	1 ⊢ (𝜑 → 𝜒)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 32417

This theorem is referenced by:  wl-syl5  32423  wl-pm2.18d  32424  wl-syl6  32430  wl-ax1  32432  wl-pm2.27  32433  wl-a1d  32439  wl-id  32441