Theorem nicodmpraw 952

Description: The inference rule for the axiom of Nicod, in raw form as explained in nicodraw 951.

Hypotheses

Ref	Expression
nicmin	⊢ φ
nicmaj	⊢ ¬ (φ ⋀ ¬ (χ ⋀ ψ))

Assertion

Ref	Expression
nicodmpraw	⊢ ψ

Proof of Theorem nicodmpraw

Step	Hyp	Ref	Expression
1		nicmin	. 2 ⊢ φ
2		nicmaj	. . . 4 ⊢ ¬ (φ ⋀ ¬ (χ ⋀ ψ))
3		iman 237	. . . 4 ⊢ ((φ → (χ ⋀ ψ)) ↔ ¬ (φ ⋀ ¬ (χ ⋀ ψ)))
4	2, 3	mpbir 190	. . 3 ⊢ (φ → (χ ⋀ ψ))
5	4	pm3.27d 325	. 2 ⊢ (φ → ψ)
6	1, 5	ax-mp 7	1 ⊢ ψ

Syntax hints:  ¬ wn 2   → wi 3   ⋀ wa 223

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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