Theorem andcomm-P3.35-L1 313

Description: Lemma for andcomm-P3.35 314. †

Assertion

Ref	Expression
andcomm-P3.35-L1	⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∧ 𝜑))

Proof of Theorem andcomm-P3.35-L1

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

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:  andcomm-P3.35  314