Theorem ncontra-P4.1 366

Description: Law of Non-contradiction. †

Assertion

Ref	Expression
ncontra-P4.1	⊢ ¬ (𝜑 ∧ ¬ 𝜑)

Proof of Theorem ncontra-P4.1

Step	Hyp	Ref	Expression
1		rcp-NDASM1of2 193	. 2 ⊢ ((𝜑 ∧ ¬ 𝜑) → 𝜑)
2		rcp-NDASM2of2 194	. 2 ⊢ ((𝜑 ∧ ¬ 𝜑) → ¬ 𝜑)
3	1, 2	rcp-NDNEGI1 218	1 ⊢ ¬ (𝜑 ∧ ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   ∧ wff-and 132

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

This theorem is referenced by:  biasandor-P4.34a  491