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Metamath Proof Explorer

Theorem sptruw

Description: Version of sp when ph is true. Instance of a1i . Uses only Tarski's FOL axiom schemes. (Contributed by NM, 23-Apr-2017)

		Ref	Expression
	Hypothesis	sptruw.1	$⊢ φ$
	Assertion	sptruw	$⊢ \forall x φ \to φ$

Step	Hyp	Ref	Expression
1		sptruw.1	$⊢ φ$
2	1	a1i	$⊢ \forall x φ \to φ$