Theorem naim2i 33735

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 33733	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜒 ⊼ 𝜓) → (𝜒 ⊼ 𝜑)))
4	1, 2, 3	mp2 9	1 ⊢ (𝜒 ⊼ 𝜑)

Syntax hints:   → wi 4   ⊼ wnan 1480

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 209  df-an 399  df-or 844  df-nan 1481

This theorem is referenced by:  naim12i  33736