Theorem rcp-NDNEGI5 222

Description: ¬ Introduction Recipe. †

Hypotheses

Ref	Expression
rcp-NDNEGI5.1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → 𝜑)
rcp-NDNEGI5.2	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → ¬ 𝜑)

Assertion

Ref	Expression
rcp-NDNEGI5	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → ¬ 𝛾₅)

Proof of Theorem rcp-NDNEGI5

Step	Hyp	Ref	Expression
1		rcp-NDNEGI5.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → 𝜑)
2	1	rcp-NDSEP5 188	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) ∧ 𝛾₅) → 𝜑)
3		rcp-NDNEGI5.2	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → ¬ 𝜑)
4	3	rcp-NDSEP5 188	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) ∧ 𝛾₅) → ¬ 𝜑)
5	2, 4	ndnegi-P3.3 168	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → ¬ 𝛾₅)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-rcp-AND4 162   ∧ 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-AND5 165

This theorem is referenced by:  rcp-RAA5  519