Theorem example-E3.1a 309

Description: Convert Sequent to Nested Implication. †

Hypothesis

Ref	Expression
example-E3.1a.1	⊢ ((𝜑₁ ∧ 𝜑₂ ∧ 𝜑₃ ∧ 𝜑₄ ∧ 𝜑₅) → 𝜓)

Assertion

Ref	Expression
example-E3.1a	⊢ (𝜑₁ → (𝜑₂ → (𝜑₃ → (𝜑₄ → (𝜑₅ → 𝜓)))))

Proof of Theorem example-E3.1a

Step	Hyp	Ref	Expression
1		example-E3.1a.1	. . . . 5 ⊢ ((𝜑₁ ∧ 𝜑₂ ∧ 𝜑₃ ∧ 𝜑₄ ∧ 𝜑₅) → 𝜓)
2	1	rcp-NDIMI5 227	. . . 4 ⊢ ((𝜑₁ ∧ 𝜑₂ ∧ 𝜑₃ ∧ 𝜑₄) → (𝜑₅ → 𝜓))
3	2	rcp-NDIMI4 226	. . 3 ⊢ ((𝜑₁ ∧ 𝜑₂ ∧ 𝜑₃) → (𝜑₄ → (𝜑₅ → 𝜓)))
4	3	rcp-NDIMI3 225	. 2 ⊢ ((𝜑₁ ∧ 𝜑₂) → (𝜑₃ → (𝜑₄ → (𝜑₅ → 𝜓))))
5	4	rcp-NDIMI2 224	1 ⊢ (𝜑₁ → (𝜑₂ → (𝜑₃ → (𝜑₄ → (𝜑₅ → 𝜓)))))

Syntax hints:   → wff-imp 10   ∧ wff-rcp-AND5 164

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

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-rcp-AND3 161  df-rcp-AND4 163  df-rcp-AND5 165

This theorem is referenced by: (None)