Theorem clav-P1.12.2AC.SH 70

Description: Another Deductive Form of clav-P1.12 68.

Hypothesis

Ref	Expression
clav-P1.12.2AC.SH.1	⊢ (𝛾₁ → (𝛾₂ → (¬ 𝜑 → 𝜑)))

Assertion

Ref	Expression
clav-P1.12.2AC.SH	⊢ (𝛾₁ → (𝛾₂ → 𝜑))

Proof of Theorem clav-P1.12.2AC.SH

Step	Hyp	Ref	Expression
1		clav-P1.12.2AC.SH.1	. 2 ⊢ (𝛾₁ → (𝛾₂ → (¬ 𝜑 → 𝜑)))
2		clav-P1.12 68	. . . . 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:  pfbycase-P1.17  88