Theorem profelimr-P4.5b.RC 388

Description: Inference Form of profelimr-P4.5b 387. †

Hypotheses

Ref	Expression
profelimr-P4.5b.RC.1	⊢ (𝜑 ∨ 𝜓)
profelimr-P4.5b.RC.2	⊢ ¬ 𝜓

Assertion

Ref	Expression
profelimr-P4.5b.RC	⊢ 𝜑

Proof of Theorem profelimr-P4.5b.RC

Step	Hyp	Ref	Expression
1		profelimr-P4.5b.RC.1	. . . 4 ⊢ (𝜑 ∨ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ∨ 𝜓))
3		profelimr-P4.5b.RC.2	. . . 4 ⊢ ¬ 𝜓
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ¬ 𝜓)
5	2, 4	profelimr-P4.5b 387	. 2 ⊢ (⊤ → 𝜑)
6	5	ndtruee-P3.18 183	1 ⊢ 𝜑

Syntax hints:  ¬ wff-neg 9   ∨ wff-or 144  ⊤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-or-D2.3 145  df-true-D2.4 155

This theorem is referenced by: (None)