Theorem nclav-P1.14.2AC.SH 75

Description: Another Deductive Form of nclav-P1.14 73.

Hypothesis

Ref	Expression
nclav-P1.14.2AC.SH.1	⊢ (𝛾₁ → (𝛾₂ → (𝜑 → ¬ 𝜑)))

Assertion

Ref	Expression
nclav-P1.14.2AC.SH	⊢ (𝛾₁ → (𝛾₂ → ¬ 𝜑))

Proof of Theorem nclav-P1.14.2AC.SH

Step	Hyp	Ref	Expression
1		nclav-P1.14.2AC.SH.1	. 2 ⊢ (𝛾₁ → (𝛾₂ → (𝜑 → ¬ 𝜑)))
2		nclav-P1.14 73	. . . . 5 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
3	2	axL1.SH 30	. . . 4 ⊢ (𝛾₂ → ((𝜑 → ¬ 𝜑) → ¬ 𝜑))
4	3	axL1.SH 30	. . 3 ⊢ (𝛾₁ → (𝛾₂ → ((𝜑 → ¬ 𝜑) → ¬ 𝜑)))
5	4	rcp-FR2.SH 42	. 2 ⊢ ((𝛾₁ → (𝛾₂ → (𝜑 → ¬ 𝜑))) → (𝛾₁ → (𝛾₂ → ¬ 𝜑)))
6	1, 5	ax-MP 14	1 ⊢ (𝛾₁ → (𝛾₂ → ¬ 𝜑))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem is referenced by:  pfbycont-P1.16  86