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Metamath Proof Explorer

Theorem albid

Description: Formula-building rule for universal quantifier (deduction form). (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	albid.1	$⊢ Ⅎ x φ$
	albid.2	$⊢ φ \to (ψ \leftrightarrow χ)$
Assertion	albid	$⊢ φ \to (\forall x ψ \leftrightarrow \forall x χ)$

Step	Hyp	Ref	Expression
1		albid.1	$⊢ Ⅎ x φ$
2		albid.2	$⊢ φ \to (ψ \leftrightarrow χ)$
3	1	nf5ri	$⊢ φ \to \forall x φ$
4	3 2	albidh	$⊢ φ \to (\forall x ψ \leftrightarrow \forall x χ)$