Metamath Proof Explorer


Axiom ax-9d2

Description: Distinct variable version of ax-6 , distinct variables case. (Contributed by Mario Carneiro, 14-Aug-2015)

Ref Expression
Assertion ax-9d2 ¬ x ¬ x = y

Detailed syntax breakdown

Step Hyp Ref Expression
0 vx setvar x
1 0 cv setvar x
2 vy setvar y
3 2 cv setvar y
4 1 3 wceq wff x = y
5 4 wn wff ¬ x = y
6 5 0 wal wff x ¬ x = y
7 6 wn wff ¬ x ¬ x = y