Theorem clav-P1.14.AC.SH 74

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

Hypothesis

Ref	Expression
nclav-P1.14.AC.SH.1	⊢ (𝛾 → (𝜑 → ¬ 𝜑))

Assertion

Ref	Expression
clav-P1.14.AC.SH	⊢ (𝛾 → ¬ 𝜑)

Proof of Theorem clav-P1.14.AC.SH

Step	Hyp	Ref	Expression
1		nclav-P1.14.AC.SH.1	. 2 ⊢ (𝛾 → (𝜑 → ¬ 𝜑))
2		nclav-P1.14 73	. . . 4 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
3	2	axL1.SH 30	. . 3 ⊢ (𝛾 → ((𝜑 → ¬ 𝜑) → ¬ 𝜑))
4	3	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → (𝜑 → ¬ 𝜑)) → (𝛾 → ¬ 𝜑))
5	1, 4	ax-MP 14	1 ⊢ (𝛾 → ¬ 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: (None)