Theorem trnsp-P3.31c.RC 286

Description: Inference Form of trnsp-P3.31c 285. †

Hypothesis

Ref	Expression
trnsp-P3.31c.RC.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
trnsp-P3.31c.RC	⊢ (¬ 𝜓 → ¬ 𝜑)

Proof of Theorem trnsp-P3.31c.RC

Step	Hyp	Ref	Expression
1		trnsp-P3.31c.RC.1	. . . 4 ⊢ (𝜑 → 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → 𝜓))
3	2	trnsp-P3.31c 285	. 2 ⊢ (⊤ → (¬ 𝜓 → ¬ 𝜑))
4	3	ndtruee-P3.18 183	1 ⊢ (¬ 𝜓 → ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10  ⊤wff-true 153

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:  allnegex-P7-L2  957