Theorem ax6fromc10 34181

Description: Rederivation of axiom ax-6 1888 from ax-c7 34170, ax-c10 34171, ax-gen 1722 and propositional calculus. See axc10 2252 for the derivation of ax-c10 34171 from ax-6 1888. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 14-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax6fromc10	|- -. A. x -. x = y

Proof of Theorem ax6fromc10

Step	Hyp	Ref	Expression
1		ax-c10 34171	. 2 |- ( A. x ( x = y -> A. x -. A. x -. x = y ) -> -. A. x -. x = y )
2		ax-c7 34170	. . 3 |- ( -. A. x -. A. x -. x = y -> -. x = y )
3	2	con4i 113	. 2 |- ( x = y -> A. x -. A. x -. x = y )
4	1, 3	mpg 1724	1 |- -. A. x -. x = y

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-3 8  ax-gen 1722  ax-c7 34170  ax-c10 34171

This theorem is referenced by:  equidqe  34207