Axiom ax-in2 605

Description: 'Not' elimination. One of the axioms of propositional logic. (Contributed by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
ax-in2	⊢ (¬ 𝜑 → (𝜑 → 𝜓))

Detailed syntax breakdown of Axiom ax-in2

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2	1	wn 3	. 2 wff ¬ 𝜑
3		wps	. . 3 wff 𝜓
4	1, 3	wi 4	. 2 wff (𝜑 → 𝜓)
5	2, 4	wi 4	1 wff (¬ 𝜑 → (𝜑 → 𝜓))

This axiom is referenced by:  pm2.21  607  con2d  614  imorr  711  dcim  827  condcOLD  840  pm5.14dc  897  pm5.54dc  904  mon  2029  difin  3318  indifdir  3337  sosng  4620  iotanul  5111