Theorem ndbii-P3.13.CL 248

Description: Closed Form of ndbii-P3.13 178. †

Assertion

Ref	Expression
ndbii-P3.13.CL	⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → (𝜑 ↔ 𝜓))

Proof of Theorem ndbii-P3.13.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of2 193	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → (𝜑 → 𝜓))
2		rcp-NDASM2of2 194	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → (𝜓 → 𝜑))
3	1, 2	ndbii-P3.13 178	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜑)) → (𝜑 ↔ 𝜓))

Syntax hints:   → wff-imp 10   ↔ 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:  dfbi-P3.47  358