Theorem nic-isw2 1446

Description: Inference for swapping nested terms. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nic-isw2.1	⊢ (ψ ⊼ (θ ⊼ φ))

Assertion

Ref	Expression
nic-isw2	⊢ (ψ ⊼ (φ ⊼ θ))

Proof of Theorem nic-isw2

Step	Hyp	Ref	Expression
1		nic-isw2.1	. . 3 ⊢ (ψ ⊼ (θ ⊼ φ))
2		nic-swap 1444	. . . 4 ⊢ ((φ ⊼ θ) ⊼ ((θ ⊼ φ) ⊼ (θ ⊼ φ)))
3	2	nic-imp 1440	. . 3 ⊢ ((ψ ⊼ (θ ⊼ φ)) ⊼ (((φ ⊼ θ) ⊼ ψ) ⊼ ((φ ⊼ θ) ⊼ ψ)))
4	1, 3	nic-mp 1436	. 2 ⊢ ((φ ⊼ θ) ⊼ ψ)
5	4	nic-isw1 1445	1 ⊢ (ψ ⊼ (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-bi1  1453  nic-bi2  1454  nic-luk1  1456  nic-luk2  1457