Theorem trnsp-P3.31a.CL 281

Description: Closed Form of trnsp-P3.31a 279. †

Assertion

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

Proof of Theorem trnsp-P3.31a.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ ((𝜑 → ¬ 𝜓) → (𝜑 → ¬ 𝜓))
2	1	trnsp-P3.31a 279	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-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  trnspeq-P4a  535