Theorem impoe-P4.4a.RC 378

Description: Inference Form of impoe-P4.4a 377. †

Hypothesis

Ref	Expression
impoe-P4.4a.RC.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
impoe-P4.4a.RC	⊢ (𝜑 → 𝜓)

Proof of Theorem impoe-P4.4a.RC

Step	Hyp	Ref	Expression
1		impoe-P4.4a.RC.1	. . . 4 ⊢ ¬ 𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ¬ 𝜑)
3	2	impoe-P4.4a 377	. 2 ⊢ (⊤ → (𝜑 → 𝜓))
4	3	ndtruee-P3.18 183	1 ⊢ (𝜑 → 𝜓)

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

This theorem is referenced by:  falseimpoe-P4.4c  383