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Metamath Proof Explorer

Theorem 2sbbii

Description: Infer double substitution into both sides of a logical equivalence. (Contributed by AV, 30-Jul-2023)

		Ref	Expression
	Hypothesis	sbbii.1	$⊢ φ \leftrightarrow ψ$
	Assertion	2sbbii	$⊢ [t/ x] [u/ y] φ \leftrightarrow [t/ x] [u/ y] ψ$

Step	Hyp	Ref	Expression
1		sbbii.1	$⊢ φ \leftrightarrow ψ$
2	1	sbbii	$⊢ [u/ y] φ \leftrightarrow [u/ y] ψ$
3	2	sbbii	$⊢ [t/ x] [u/ y] φ \leftrightarrow [t/ x] [u/ y] ψ$