Theorem naim1i 36961

Description: Constructor rule for ⊼. (Contributed by Anthony Hart, 2-Sep-2011.)

Hypotheses

Ref	Expression
naim1i.1	⊢ (𝜑 → 𝜓)
naim1i.2	⊢ (𝜓 ⊼ 𝜒)

Assertion

Ref	Expression
naim1i	⊢ (𝜑 ⊼ 𝜒)

Proof of Theorem naim1i

Step	Hyp	Ref	Expression
1		naim1i.1	. 2 ⊢ (𝜑 → 𝜓)
2		naim1i.2	. 2 ⊢ (𝜓 ⊼ 𝜒)
3		naim1 36959	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜓 ⊼ 𝜒) → (𝜑 ⊼ 𝜒)))
4	1, 2, 3	mp2 9	1 ⊢ (𝜑 ⊼ 𝜒)

This proof depends on syntax axioms:   → wi 4   ⊼ wnan 1521

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-nan 1522

This theorem is used by:  naim12i  36963