Theorem trnsp-P3.31d.CL 290

Description: Closed Form of trnsp-P3.31d 288 (Axiom L3).

This is a restatement of Axiom L3, deduced via natural deduction.

Assertion

Ref	Expression
trnsp-P3.31d.CL	⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑))

Proof of Theorem trnsp-P3.31d.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ ((¬ 𝜑 → ¬ 𝜓) → (¬ 𝜑 → ¬ 𝜓))
2	1	trnsp-P3.31d 288	1 ⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

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  df-rcp-AND3 161

This theorem is referenced by:  trnspeq-P4c  537