Theorem rcp-NDNEGI4 221

Description: ¬ Introduction Recipe. †

Hypotheses

Ref	Expression
rcp-NDNEGI4.1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝜑)
rcp-NDNEGI4.2	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → ¬ 𝜑)

Assertion

Ref	Expression
rcp-NDNEGI4	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → ¬ 𝛾₄)

Proof of Theorem rcp-NDNEGI4

Step	Hyp	Ref	Expression
1		rcp-NDNEGI4.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → 𝜑)
2	1	rcp-NDSEP4 187	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) ∧ 𝛾₄) → 𝜑)
3		rcp-NDNEGI4.2	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → ¬ 𝜑)
4	3	rcp-NDSEP4 187	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) ∧ 𝛾₄) → ¬ 𝜑)
5	2, 4	ndnegi-P3.3 168	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → ¬ 𝛾₄)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-rcp-AND3 160   ∧ wff-rcp-AND4 162

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-AND4 163

This theorem is referenced by:  rcp-RAA4  518