Theorem andcomm-P3.35 314

Description: '∧' Commutativity. †

Assertion

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

Proof of Theorem andcomm-P3.35

Step	Hyp	Ref	Expression
1		andcomm-P3.35-L1 313	. 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∧ 𝜑))
2		andcomm-P3.35-L1 313	. 2 ⊢ ((𝜓 ∧ 𝜑) → (𝜑 ∧ 𝜓))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))

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:  subandr-P3.42b  341  idandtruer-P4.19b  439  biasandor-P4.34a  491  andcomm2-P4  564