Theorem naim2i 36394

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

Hypotheses

Ref	Expression
naim2i.1	⊢ (𝜑 → 𝜓)
naim2i.2	⊢ (𝜒 ⊼ 𝜓)

Assertion

Ref	Expression
naim2i	⊢ (𝜒 ⊼ 𝜑)

Proof of Theorem naim2i

Step	Hyp	Ref	Expression
1		naim2i.1	. 2 ⊢ (𝜑 → 𝜓)
2		naim2i.2	. 2 ⊢ (𝜒 ⊼ 𝜓)
3		naim2 36392	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜒 ⊼ 𝜓) → (𝜒 ⊼ 𝜑)))
4	1, 2, 3	mp2 9	1 ⊢ (𝜒 ⊼ 𝜑)

Syntax hints:   → wi 4   ⊼ wnan 1490

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-nan 1491

This theorem is referenced by:  naim12i  36395