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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	$⊢ \forall x x = y \to ([x/ z] φ \leftrightarrow [y/ z] φ)$

Proof

Step	Hyp	Ref	Expression
1		sbequ	$⊢ x = y \to ([x/ z] φ \leftrightarrow [y/ z] φ)$
2	1	sps	$⊢ \forall x x = y \to ([x/ z] φ \leftrightarrow [y/ z] φ)$