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Metamath Proof Explorer

Theorem drsb2

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of Megill p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005)

		Ref	Expression
	Assertion	drsb2	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( [ 𝑥 / 𝑧 ] 𝜑 ↔ [ 𝑦 / 𝑧 ] 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		sbequ	⊢ ( 𝑥 = 𝑦 → ( [ 𝑥 / 𝑧 ] 𝜑 ↔ [ 𝑦 / 𝑧 ] 𝜑 ) )
2	1	sps	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( [ 𝑥 / 𝑧 ] 𝜑 ↔ [ 𝑦 / 𝑧 ] 𝜑 ) )