Theorem nandir-P4.3b.RC 376

Description: Inference Form of nandir-P4.3b 375. †

Hypothesis

Ref	Expression
nandir-P4.3b.RC.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
nandir-P4.3b.RC	⊢ ¬ (𝜑 ∧ 𝜓)

Proof of Theorem nandir-P4.3b.RC

Step	Hyp	Ref	Expression
1		nandir-P4.3b.RC.1	. . . 4 ⊢ ¬ 𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ¬ 𝜑)
3	2	nandir-P4.3b 375	. 2 ⊢ (⊤ → ¬ (𝜑 ∧ 𝜓))
4	3	ndtruee-P3.18 183	1 ⊢ ¬ (𝜑 ∧ 𝜓)

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)