Theorem orcomm-P3.37 319

Description: '∨' Commutativity. †

Assertion

Ref	Expression
orcomm-P3.37	⊢ ((𝜑 ∨ 𝜓) ↔ (𝜓 ∨ 𝜑))

Proof of Theorem orcomm-P3.37

Step	Hyp	Ref	Expression
1		orcomm-P3.37-L1 318	. 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))
2		orcomm-P3.37-L1 318	. 2 ⊢ ((𝜓 ∨ 𝜑) → (𝜑 ∨ 𝜓))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 ∨ 𝜓) ↔ (𝜓 ∨ 𝜑))

Syntax hints:   ↔ wff-bi 104   ∨ wff-or 144

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-or-D2.3 145  df-true-D2.4 155

This theorem is referenced by:  suborr-P3.43b  348  idorfalser-P4.20b  441  biasandor-P4.34a  491  orcomm2-P4  566  dfnfreealt-P6  683  nfrneg-P6  688  dfnfree-P7  968  dfnfreeint-P7  969