Theorem nabi2i 36418

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

Hypotheses

Ref	Expression
nabi2i.1	⊢ (𝜑 ↔ 𝜓)
nabi2i.2	⊢ (𝜒 ⊼ 𝜓)

Assertion

Ref	Expression
nabi2i	⊢ (𝜒 ⊼ 𝜑)

Proof of Theorem nabi2i

Step	Hyp	Ref	Expression
1		nabi2i.2	. 2 ⊢ (𝜒 ⊼ 𝜓)
2		nabi2i.1	. . . 4 ⊢ (𝜑 ↔ 𝜓)
3	2	bicomi 224	. . 3 ⊢ (𝜓 ↔ 𝜑)
4	3	nanbi2i 1505	. 2 ⊢ ((𝜒 ⊼ 𝜓) ↔ (𝜒 ⊼ 𝜑))
5	1, 4	mpbi 230	1 ⊢ (𝜒 ⊼ 𝜑)

Syntax hints:   ↔ wb 206   ⊼ wnan 1491

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-nan 1492

This theorem is referenced by:  nabi12i  36419