Theorem sptruw 1671

Description: Version of sp 1747 when φ is true. 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 10	1 ⊢ (∀xφ → φ)

This proof depends on syntax axioms:   → wi 4  ∀wal 1540

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

This theorem is used by: (None)