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Metamath Proof Explorer

Theorem ax9v

Description: Weakened version of ax-9 , with a disjoint variable condition on x , y . This should be the only proof referencing ax-9 , and it should be referenced only by its two weakened versions ax9v1 and ax9v2 , from which ax-9 is then rederived as ax9 , which shows that either ax9v or the conjunction of ax9v1 and ax9v2 is sufficient. (Contributed by BJ, 7-Dec-2020) Use ax9 instead. (New usage is discouraged.)

		Ref	Expression
	Assertion	ax9v	⊢ ( 𝑥 = 𝑦 → ( 𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦 ) )

Proof

Step	Hyp	Ref	Expression
1		ax-9	⊢ ( 𝑥 = 𝑦 → ( 𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦 ) )