Description: Rederivation of Axiom ax-6 from ax-c7 , ax-c10 , ax-gen and propositional calculus. See axc10 for the derivation of ax-c10 from ax-6 . Lemma L18 in Megill p. 446 (p. 14 of the preprint). (Contributed by NM, 14-May-1993) (Proof modification is discouraged.) Use ax-6 instead. (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ax6fromc10 | |- -. A. x -. x = y |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-c10 | |- ( A. x ( x = y -> A. x -. A. x -. x = y ) -> -. A. x -. x = y ) |
|
| 2 | ax-c7 | |- ( -. A. x -. A. x -. x = y -> -. x = y ) |
|
| 3 | 2 | con4i | |- ( x = y -> A. x -. A. x -. x = y ) |
| 4 | 1 3 | mpg | |- -. A. x -. x = y |