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Metamath Proof Explorer

Theorem sbid2v

Description: An identity law for substitution. Used in proof of Theorem 9.7 of Megill p. 449 (p. 16 of the preprint). Usage of this theorem is discouraged because it depends on ax-13 . See sbid2vw for a version with an extra disjoint variable condition requiring fewer axioms. (Contributed by NM, 5-Aug-1993) (New usage is discouraged.)

		Ref	Expression
	Assertion	sbid2v	⊢ ( [ 𝑦 / 𝑥 ] [ 𝑥 / 𝑦 ] 𝜑 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfv	⊢ Ⅎ 𝑥 𝜑
2	1	sbid2	⊢ ( [ 𝑦 / 𝑥 ] [ 𝑥 / 𝑦 ] 𝜑 ↔ 𝜑 )