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Metamath Proof Explorer

Theorem dveeq2ALT

Description: Alternate proof of dveeq2 , shorter but requiring ax-11 . (Contributed by NM, 2-Jan-2002) (Revised by NM, 20-Jul-2015) (New usage is discouraged.) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	dveeq2ALT	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ( 𝑧 = 𝑦 → ∀ 𝑥 𝑧 = 𝑦 ) )

Proof

Step	Hyp	Ref	Expression
1		equequ2	⊢ ( 𝑤 = 𝑦 → ( 𝑧 = 𝑤 ↔ 𝑧 = 𝑦 ) )
2	1	dvelimv	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ( 𝑧 = 𝑦 → ∀ 𝑥 𝑧 = 𝑦 ) )