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Metamath Proof Explorer

Theorem fnoprab

Description: Functionality and domain of an operation class abstraction. (Contributed by NM, 15-May-1995)

		Ref	Expression
	Hypothesis	fnoprab.1	$⊢ φ \to \exists! z ψ$
	Assertion	fnoprab	$⊢ \{⟨⟨x, y⟩, z⟩ \| (φ \land ψ)\} Fn \{⟨x, y⟩ \| φ\}$

Step	Hyp	Ref	Expression
1		fnoprab.1	$⊢ φ \to \exists! z ψ$
2	1	gen2	$⊢ \forall x \forall y (φ \to \exists! z ψ)$
3		fnoprabg	$⊢ \forall x \forall y (φ \to \exists! z ψ) \to \{⟨⟨x, y⟩, z⟩ \| (φ \land ψ)\} Fn \{⟨x, y⟩ \| φ\}$
4	2 3	ax-mp	$⊢ \{⟨⟨x, y⟩, z⟩ \| (φ \land ψ)\} Fn \{⟨x, y⟩ \| φ\}$