Theorem wl-luk-syl 37359

Description: An inference version of the transitive laws for implication luk-1 1654. 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-luk-syl.1	⊢ (𝜑 → 𝜓)
wl-luk-syl.2	⊢ (𝜓 → 𝜒)

Assertion

Ref	Expression
wl-luk-syl	⊢ (𝜑 → 𝜒)

Proof of Theorem wl-luk-syl

Step	Hyp	Ref	Expression
1		wl-luk-syl.2	. 2 ⊢ (𝜓 → 𝜒)
2		wl-luk-syl.1	. . 3 ⊢ (𝜑 → 𝜓)
3	2	wl-luk-imim1i 37358	. 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 37354

This theorem is referenced by:  wl-luk-imtrid  37360  wl-luk-pm2.18d  37361  wl-luk-imtrdi  37367  wl-luk-ax1  37369  wl-luk-pm2.27  37370  wl-luk-a1d  37376  wl-luk-id  37378