Theorem nprofelimr-P4.6b.RC 392

Description: Inference Form of nprofelimr-P4.6b 391. †

Hypotheses

Ref	Expression
nprofelimr-P4.6b.RC.1	⊢ ¬ (𝜑 ∧ 𝜓)
nprofelimr-P4.6b.RC.2	⊢ 𝜓

Assertion

Ref	Expression
nprofelimr-P4.6b.RC	⊢ ¬ 𝜑

Proof of Theorem nprofelimr-P4.6b.RC

Step	Hyp	Ref	Expression
1		nprofelimr-P4.6b.RC.1	. . . 4 ⊢ ¬ (𝜑 ∧ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ¬ (𝜑 ∧ 𝜓))
3		nprofelimr-P4.6b.RC.2	. . . 4 ⊢ 𝜓
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝜓)
5	2, 4	nprofelimr-P4.6b 391	. 2 ⊢ (⊤ → ¬ 𝜑)
6	5	ndtruee-P3.18 183	1 ⊢ ¬ 𝜑

Syntax hints:  ¬ wff-neg 9   ∧ wff-and 132  ⊤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: (None)