This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 19.21bi

Description: Inference form of 19.21 and also deduction form of sp . (Contributed by NM, 26-May-1993)

Ref Expression
Hypothesis 19.21bi.1 ⊢ ( 𝜑 → ∀ 𝑥 𝜓 )
Assertion 19.21bi ( 𝜑 → 𝜓 )

Proof

Step Hyp Ref Expression
1 19.21bi.1 ⊢ ( 𝜑 → ∀ 𝑥 𝜓 )
2 sp ⊢ ( ∀ 𝑥 𝜓 → 𝜓 )
3 1 2 syl ⊢ ( 𝜑 → 𝜓 )