Theorem rcp-FALSENEGI5 437

Description: '¬' Introduction with '⊥'. †

Hypothesis

Ref	Expression
rcp-FALSENEGI5.1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → ⊥)

Assertion

Ref	Expression
rcp-FALSENEGI5	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → ¬ 𝛾₅)

Proof of Theorem rcp-FALSENEGI5

Step	Hyp	Ref	Expression
1		rcp-FALSENEGI5.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄ ∧ 𝛾₅) → ⊥)
2	1	rcp-NDSEP5 188	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) ∧ 𝛾₅) → ⊥)
3	2	falsenegi-P4.18 432	1 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃ ∧ 𝛾₄) → ¬ 𝛾₅)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10  ⊥wff-false 157   ∧ 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-true-D2.4 155  df-false-D2.5 158  df-rcp-AND5 165

This theorem is referenced by:  rcp-FALSERAA5  525