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Metamath Proof Explorer

Theorem rabbidv

Description: Equivalent wff's yield equal restricted class abstractions (deduction form). (Contributed by NM, 10-Feb-1995)

		Ref	Expression
	Hypothesis	rabbidv.1	$⊢ φ \to (ψ \leftrightarrow χ)$
	Assertion	rabbidv	$⊢ φ \to \{x \in A \| ψ\} = \{x \in A \| χ\}$

Step	Hyp	Ref	Expression
1		rabbidv.1	$⊢ φ \to (ψ \leftrightarrow χ)$
2	1	adantr	$⊢ (φ \land x \in A) \to (ψ \leftrightarrow χ)$
3	2	rabbidva	$⊢ φ \to \{x \in A \| ψ\} = \{x \in A \| χ\}$