Axiom ax-luk2 35518

Description: 2 of 3 axioms for propositional calculus due to Lukasiewicz. Copy of luk-2 1660 or pm2.18 128, but introduced as an axiom. The core idea behind this axiom is, that if something can be implied from both an antecedent, and separately from its negation, then the antecedent is irrelevant to the consequent, and can safely be dropped. This is perhaps better seen from the following slightly extended version (related to pm2.65 192):

((𝜑 → 𝜑) → ((¬ 𝜑 → 𝜑) → 𝜑)). (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-luk2	⊢ ((¬ 𝜑 → 𝜑) → 𝜑)

Detailed syntax breakdown of Axiom ax-luk2

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2	1	wn 3	. 2 wff ¬ 𝜑
3	2, 1, 1	bj-0 34649	1 wff ((¬ 𝜑 → 𝜑) → 𝜑)

This axiom is referenced by:  wl-luk-pm2.18d  35524  wl-luk-ax3  35531  wl-luk-pm2.27  35533  wl-luk-id  35541