Theorem rcp-FALSENEGI3 435

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

Hypothesis

Ref	Expression
rcp-FALSENEGI3.1	⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → ⊥)

Assertion

Ref	Expression
rcp-FALSENEGI3	⊢ ((𝛾₁ ∧ 𝛾₂) → ¬ 𝛾₃)

Proof of Theorem rcp-FALSENEGI3

Step	Hyp	Ref	Expression
1		rcp-FALSENEGI3.1	. . 3 ⊢ ((𝛾₁ ∧ 𝛾₂ ∧ 𝛾₃) → ⊥)
2	1	rcp-NDSEP3 186	. 2 ⊢ (((𝛾₁ ∧ 𝛾₂) ∧ 𝛾₃) → ⊥)
3	2	falsenegi-P4.18 432	1 ⊢ ((𝛾₁ ∧ 𝛾₂) → ¬ 𝛾₃)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-and 132  ⊥wff-false 157   ∧ wff-rcp-AND3 160

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-AND3 161

This theorem is referenced by:  rcp-FALSERAA3  523