Theorem andassoc-P3.36-L2 316

Description: Lemma for andassoc-P3.36 317. †

Assertion

Ref	Expression
andassoc-P3.36-L2	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → ((𝜑 ∧ 𝜓) ∧ 𝜒))

Proof of Theorem andassoc-P3.36-L2

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. . . 4 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜑 ∧ (𝜓 ∧ 𝜒)))
2	1	ndander-P3.9 174	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜑)
3	1	ndandel-P3.8 173	. . . 4 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜓 ∧ 𝜒))
4	3	ndander-P3.9 174	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜓)
5	2, 4	ndandi-P3.7 172	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → (𝜑 ∧ 𝜓))
6	3	ndandel-P3.8 173	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜒)
7	5, 6	ndandi-P3.7 172	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → ((𝜑 ∧ 𝜓) ∧ 𝜒))

Syntax hints:   → wff-imp 10   ∧ 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:  andassoc-P3.36  317