Theorem wl-luk-pm2.04 38119

Description: Swap antecedents. Theorem *2.04 of [WhiteheadRussell] p. 100. This was the third axiom in Frege's logic system, specifically Proposition 8 of [Frege1879] p. 35. Copy of pm2.04 91 with a different proof. (Contributed by Wolf Lammen, 7-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-luk-pm2.04	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))

Proof of Theorem wl-luk-pm2.04

Step	Hyp	Ref	Expression
1		wl-luk-ax1 38108	. 2 ⊢ (𝜓 → (𝜑 → 𝜓))
2		wl-luk-ax2 38116	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
3	1, 2	wl-luk-imtrid 38099	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (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-impchain-com-1.2  38127  wl-impchain-com-1.3  38128  wl-impchain-com-1.4  38129