Theorem andassoc-P3.36 317

Description: '∧' Associativity. †

Assertion

Ref	Expression
andassoc-P3.36	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))

Proof of Theorem andassoc-P3.36

Step	Hyp	Ref	Expression
1		andassoc-P3.36-L1 315	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → (𝜑 ∧ (𝜓 ∧ 𝜒)))
2		andassoc-P3.36-L2 316	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → ((𝜑 ∧ 𝜓) ∧ 𝜒))
3	1, 2	rcp-NDBII0 239	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))

Syntax hints:   ↔ wff-bi 104   ∧ 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:  andassoc2a-P4  568  andassoc2b-P4  570