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Metamath Proof Explorer

Theorem dfrel5

Description: Alternate definition of the relation predicate. (Contributed by Peter Mazsa, 6-Nov-2018)

		Ref	Expression
	Assertion	dfrel5	$⊢ Rel R \leftrightarrow {R ↾}_{dom R} = R$

Step	Hyp	Ref	Expression
1		dfrel2	$⊢ Rel R \leftrightarrow {R^{-1}}^{-1} = R$
2		resdm2	$⊢ {R ↾}_{dom R} = {R^{-1}}^{-1}$
3	2	eqeq1i	$⊢ {R ↾}_{dom R} = R \leftrightarrow {R^{-1}}^{-1} = R$
4	1 3	bitr4i	$⊢ Rel R \leftrightarrow {R ↾}_{dom R} = R$