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Metamath Proof Explorer

Theorem ax8v

Description: Weakened version of ax-8 , with a disjoint variable condition on x , y . This should be the only proof referencing ax-8 , and it should be referenced only by its two weakened versions ax8v1 and ax8v2 , from which ax-8 is then rederived as ax8 , which shows that either ax8v or the conjunction of ax8v1 and ax8v2 is sufficient. (Contributed by BJ, 7-Dec-2020) Use ax8 instead. (New usage is discouraged.)

		Ref	Expression
	Assertion	ax8v	⊢ ( 𝑥 = 𝑦 → ( 𝑥 ∈ 𝑧 → 𝑦 ∈ 𝑧 ) )

Proof

Step	Hyp	Ref	Expression
1		ax-8	⊢ ( 𝑥 = 𝑦 → ( 𝑥 ∈ 𝑧 → 𝑦 ∈ 𝑧 ) )