Theorem sptruw 1839

Description: Version of sp 2222 when 𝜑 is true. Instance of a1i 11. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 23-Apr-2017.)

Hypothesis

Ref	Expression
sptruw.1	⊢ 𝜑

Assertion

Ref	Expression
sptruw	⊢ (∀𝑥𝜑 → 𝜑)

Proof of Theorem sptruw

Step	Hyp	Ref	Expression
1		sptruw.1	. 2 ⊢ 𝜑
2	1	a1i 11	1 ⊢ (∀𝑥𝜑 → 𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6

This theorem is used by: (None)