Description: Show that the original axiom ax-c10 can be derived from ax6 and axc7 (on top of propositional calculus, ax-gen , and ax-4 ). See ax6fromc10 for the rederivation of ax6 from ax-c10 .
Normally, axc10 should be used rather than ax-c10 , except by theorems specifically studying the latter's properties. Usage of this theorem has been discouraged later on to avoid ax-13 propagation. Check out bj-axc10v for a weaker version requiring less axioms. (Contributed by NM, 5-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | axc10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6 | ||
2 | con3 | ||
3 | 2 | al2imi | |
4 | 1 3 | mtoi | |
5 | axc7 | ||
6 | 4 5 | syl |