Metamath Proof Explorer


Theorem ax6dgen

Description: Tarski's system uses the weaker ax6v instead of the bundled ax-6 , so here we show that the degenerate case of ax-6 can be derived. Even though ax-6 is in the list of axioms used, recall that in set.mm, the only statement referencing ax-6 is ax6v . We later rederive from ax6v the bundled form as ax6 with the help of the auxiliary axiom schemes. (Contributed by NM, 23-Apr-2017)

Ref Expression
Assertion ax6dgen
|- -. A. x -. x = x

Proof

Step Hyp Ref Expression
1 equid
 |-  x = x
2 1 notnoti
 |-  -. -. x = x
3 2 spfalw
 |-  ( A. x -. x = x -> -. x = x )
4 1 3 mt2
 |-  -. A. x -. x = x