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Metamath Proof Explorer

Theorem rabbia2

Description: Equivalent wff's yield equal restricted class abstractions. (Contributed by Glauco Siliprandi, 26-Jun-2021)

		Ref	Expression
	Hypothesis	rabbia2.1	$⊢ (x \in A \land ψ) \leftrightarrow (x \in B \land χ)$
	Assertion	rabbia2	$⊢ \{x \in A \| ψ\} = \{x \in B \| χ\}$

Step	Hyp	Ref	Expression
1		rabbia2.1	$⊢ (x \in A \land ψ) \leftrightarrow (x \in B \land χ)$
2	1	a1i	$⊢ ⊤ \to ((x \in A \land ψ) \leftrightarrow (x \in B \land χ))$
3	2	rabbidva2	$⊢ ⊤ \to \{x \in A \| ψ\} = \{x \in B \| χ\}$
4	3	mptru	$⊢ \{x \in A \| ψ\} = \{x \in B \| χ\}$