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Metamath Proof Explorer

Theorem rabbii

Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv . (Contributed by Peter Mazsa, 1-Nov-2019)

		Ref	Expression
	Hypothesis	rabbii.1	$⊢ φ \leftrightarrow ψ$
	Assertion	rabbii	$⊢ \{x \in A \| φ\} = \{x \in A \| ψ\}$

Proof

Step	Hyp	Ref	Expression
1		rabbii.1	$⊢ φ \leftrightarrow ψ$
2	1	a1i	$⊢ x \in A \to (φ \leftrightarrow ψ)$
3	2	rabbiia	$⊢ \{x \in A \| φ\} = \{x \in A \| ψ\}$