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Metamath Proof Explorer

Theorem ax13dgen1

Description: Degenerate instance of ax-13 where bundled variables x and y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017)

		Ref	Expression
	Assertion	ax13dgen1	⊢ ( ¬ 𝑥 = 𝑥 → ( 𝑥 = 𝑧 → ∀ 𝑥 𝑥 = 𝑧 ) )

Proof

Step	Hyp	Ref	Expression
1		equid	⊢ 𝑥 = 𝑥
2	1	pm2.24i	⊢ ( ¬ 𝑥 = 𝑥 → ( 𝑥 = 𝑧 → ∀ 𝑥 𝑥 = 𝑧 ) )