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	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		sptruw.1	⊢ 𝜑
2	1	a1i	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )