Axiom ax-in2 615

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

Assertion

Ref	Expression
ax-in2	|- ( -. ph -> ( ph -> ps ) )

Detailed syntax breakdown of Axiom ax-in2

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2	1	wn 3	. 2 wff -. ph
3		wps	. . 3 wff ps
4	1, 3	wi 4	. 2 wff ( ph -> ps )
5	2, 4	wi 4	1 wff ( -. ph -> ( ph -> ps ) )

This axiom is referenced by:  pm2.21  617  con2d  624  imorr  721  dcim  841  condcOLD  854  pm5.14dc  911  pm5.54dc  918  mon  2055  difin  3374  indifdir  3393  sosng  4701  iotanul  5195