Theorem nic-isw1 1445

Description: Inference version of nic-swap 1444. (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 1444	. 2 ⊢ ((θ ⊼ φ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ)))
3	1, 2	nic-mp 1436	1 ⊢ (φ ⊼ θ)

Syntax hints:   ⊼ wnan 1287

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 177  df-an 360  df-nan 1288

This theorem is referenced by:  nic-isw2  1446  nic-iimp1  1447  nic-iimp2  1448  nic-idel  1449  nic-ich  1450  nic-luk2  1457