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Metamath Proof Explorer

Theorem sbid2vw

Description: Reverting substitution yields the original expression. Based on fewer axioms than sbid2v , at the expense of an extra distinct variable condition. (Contributed by NM, 14-May-1993) (Revised by Wolf Lammen, 5-Aug-2023)

		Ref	Expression
	Assertion	sbid2vw	⊢ ( [ 𝑡 / 𝑥 ] [ 𝑥 / 𝑡 ] 𝜑 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		sbequ12r	⊢ ( 𝑥 = 𝑡 → ( [ 𝑥 / 𝑡 ] 𝜑 ↔ 𝜑 ) )
2	1	sbievw	⊢ ( [ 𝑡 / 𝑥 ] [ 𝑥 / 𝑡 ] 𝜑 ↔ 𝜑 )