Theorem bj-axc14

Description: Alternate proof of axc14 (even when inlining the above results, this gives a shorter proof). (Contributed by BJ, 20-Oct-2021) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-axc14	|- ( -. A. z z = x -> ( -. A. z z = y -> ( x e. y -> A. z x e. y ) ) )

Proof

Step	Hyp	Ref	Expression
1		bj-axc14nf	|- ( -. A. z z = x -> ( -. A. z z = y -> F/ z x e. y ) )
2		nf5r	|- ( F/ z x e. y -> ( x e. y -> A. z x e. y ) )
3	2	a1i	|- ( -. A. z z = x -> ( F/ z x e. y -> ( x e. y -> A. z x e. y ) ) )
4	1 3	syld	|- ( -. A. z z = x -> ( -. A. z z = y -> ( x e. y -> A. z x e. y ) ) )