Theorem wl-com12 32434

Description: Inference that swaps (commutes) antecedents in an implication. Copy of com12 32 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

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

Assertion

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

Proof of Theorem wl-com12

Step	Hyp	Ref	Expression
1		wl-com12.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		wl-pm2.27 32433	. 2 ⊢ (𝜓 → ((𝜓 → 𝜒) → 𝜒))
3	1, 2	wl-syl5 32423	1 ⊢ (𝜓 → (𝜑 → 𝜒))

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-pm2.21  32435  wl-imim2  32438