Theorem bisym-P3.33b.CL.SYM 301

Description: Closed Symmetric Form of bisym-P3.33b 298. †

Assertion

Ref	Expression
bisym-P3.33b.CL.SYM	⊢ ((𝜑 ↔ 𝜓) ↔ (𝜓 ↔ 𝜑))

Proof of Theorem bisym-P3.33b.CL.SYM

Step	Hyp	Ref	Expression
1		bisym-P3.33b.CL 300	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑))
2		bisym-P3.33b.CL 300	. 2 ⊢ ((𝜓 ↔ 𝜑) → (𝜑 ↔ 𝜓))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 ↔ 𝜓) ↔ (𝜓 ↔ 𝜑))

Syntax hints:   ↔ wff-bi 104

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:  subbir-P3.41b  334