Theorem nic-isw1 1702

Description: Inference version of nic-swap 1701. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nic-isw1.1	⊢ (𝜃 ⊼ 𝜑)

Assertion

Ref	Expression
nic-isw1	⊢ (𝜑 ⊼ 𝜃)

Proof of Theorem nic-isw1

Step	Hyp	Ref	Expression
1		nic-isw1.1	. 2 ⊢ (𝜃 ⊼ 𝜑)
2		nic-swap 1701	. 2 ⊢ ((𝜃 ⊼ 𝜑) ⊼ ((𝜑 ⊼ 𝜃) ⊼ (𝜑 ⊼ 𝜃)))
3	1, 2	nic-mp 1693	1 ⊢ (𝜑 ⊼ 𝜃)

Syntax hints:   ⊼ wnan 1513

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 400  df-nan 1514

This theorem is referenced by:  nic-isw2  1703  nic-iimp1  1704  nic-iimp2  1705  nic-idel  1706  nic-ich  1707  nic-luk2  1714