Theorem nic-idbl 1451

Description: Double the terms. Since doubling is the same as negation, this can be viewed as a contraposition inference. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
nic-idbl	⊢ ((ψ ⊼ ψ) ⊼ ((φ ⊼ φ) ⊼ (φ ⊼ φ)))

Proof of Theorem nic-idbl

Step	Hyp	Ref	Expression
1		nic-idbl.1	. . 3 ⊢ (φ ⊼ (ψ ⊼ ψ))
2	1	nic-imp 1440	. 2 ⊢ ((ψ ⊼ ψ) ⊼ ((φ ⊼ ψ) ⊼ (φ ⊼ ψ)))
3	1	nic-imp 1440	. 2 ⊢ ((φ ⊼ ψ) ⊼ ((φ ⊼ φ) ⊼ (φ ⊼ φ)))
4	2, 3	nic-ich 1450	1 ⊢ ((ψ ⊼ ψ) ⊼ ((φ ⊼ φ) ⊼ (φ ⊼ φ)))

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-luk1  1456