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Metamath Proof Explorer

Theorem trujust

Description: Soundness justification theorem for df-tru . Instance of monothetic . (Contributed by Mario Carneiro, 17-Nov-2013) (Revised by NM, 11-Jul-2019)

		Ref	Expression
	Assertion	trujust	$⊢ (\forall x x = x \to \forall x x = x) \leftrightarrow (\forall y y = y \to \forall y y = y)$

Proof

Step	Hyp	Ref	Expression
1		monothetic	$⊢ (\forall x x = x \to \forall x x = x) \leftrightarrow (\forall y y = y \to \forall y y = y)$