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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	$⊢ [t/ x] [x/ t] φ \leftrightarrow φ$

Proof

Step	Hyp	Ref	Expression
1		sbequ12r	$⊢ x = t \to ([x/ t] φ \leftrightarrow φ)$
2	1	sbievw	$⊢ [t/ x] [x/ t] φ \leftrightarrow φ$