Theorem ndbier-P3.15.CL 250

Description: Closed Form of ndbier-P3.15 180. †

Assertion

Ref	Expression
ndbier-P3.15.CL	⊢ ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑))

Proof of Theorem ndbier-P3.15.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	ndbier-P3.15 180	1 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑))

Syntax hints:   → wff-imp 10   ↔ 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:  dfbi-P3.47  358  truthtblfbit-P4.39c  509