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Metamath Proof Explorer

Theorem naev

Description: If some set variables can assume different values, then any two distinct set variables cannot always be the same. (Contributed by Wolf Lammen, 10-Aug-2019)

		Ref	Expression
	Assertion	naev	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ¬ ∀ 𝑢 𝑢 = 𝑣 )

Proof

Step	Hyp	Ref	Expression
1		aev	⊢ ( ∀ 𝑢 𝑢 = 𝑣 → ∀ 𝑥 𝑥 = 𝑦 )
2	1	con3i	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ¬ ∀ 𝑢 𝑢 = 𝑣 )