Theorem naim12i 37181

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

Hypotheses

Ref	Expression
naim12i.1	⊢ (𝜑 → 𝜓)
naim12i.2	⊢ (𝜒 → 𝜃)
naim12i.3	⊢ (𝜓 ⊼ 𝜃)

Assertion

Ref	Expression
naim12i	⊢ (𝜑 ⊼ 𝜒)

Proof of Theorem naim12i

Step	Hyp	Ref	Expression
1		naim12i.2	. 2 ⊢ (𝜒 → 𝜃)
2		naim12i.1	. . 3 ⊢ (𝜑 → 𝜓)
3		naim12i.3	. . 3 ⊢ (𝜓 ⊼ 𝜃)
4	2, 3	naim1i 37179	. 2 ⊢ (𝜑 ⊼ 𝜃)
5	1, 4	naim2i 37180	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: (None)