Theorem wl-luk-com12 38110

Description: Inference that swaps (commutes) antecedents in an implication. Copy of com12 33 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-luk-com12.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
wl-luk-com12	⊢ (𝜓 → (𝜑 → 𝜒))

Proof of Theorem wl-luk-com12

Step	Hyp	Ref	Expression
1		wl-luk-com12.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		wl-luk-pm2.27 38109	. 2 ⊢ (𝜓 → ((𝜓 → 𝜒) → 𝜒))
3	1, 2	wl-luk-imtrid 38099	1 ⊢ (𝜓 → (𝜑 → 𝜒))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38093  ax-luk2 38094  ax-luk3 38095

This theorem is used by:  wl-luk-pm2.21  38111  wl-luk-imim2  38114