Theorem bj-ax6elem2

Description: Lemma for bj-ax6e . (Contributed by BJ, 22-Dec-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-ax6elem2	⊢ ( ∀ 𝑥 𝑦 = 𝑧 → ∃ 𝑥 𝑥 = 𝑦 )

Proof

Step	Hyp	Ref	Expression
1		ax6ev	⊢ ∃ 𝑥 𝑥 = 𝑧
2		equeucl	⊢ ( 𝑥 = 𝑧 → ( 𝑦 = 𝑧 → 𝑥 = 𝑦 ) )
3	1 2	eximii	⊢ ∃ 𝑥 ( 𝑦 = 𝑧 → 𝑥 = 𝑦 )
4	3	19.35i	⊢ ( ∀ 𝑥 𝑦 = 𝑧 → ∃ 𝑥 𝑥 = 𝑦 )