Theorem rcp-NDANDI0 229

Description: '∧' Introduction. †

Hypotheses

Ref	Expression
rcp-NDANDI0.1	⊢ 𝜑
rcp-NDANDI0.2	⊢ 𝜓

Assertion

Ref	Expression
rcp-NDANDI0	⊢ (𝜑 ∧ 𝜓)

Proof of Theorem rcp-NDANDI0

Step	Hyp	Ref	Expression
1		rcp-NDANDI0.1	. . . 4 ⊢ 𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝜑)
3		rcp-NDANDI0.2	. . . 4 ⊢ 𝜓
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝜓)
5	2, 4	ndandi-P3.7 172	. 2 ⊢ (⊤ → (𝜑 ∧ 𝜓))
6	5	ndtruee-P3.18 183	1 ⊢ (𝜑 ∧ 𝜓)

Syntax hints:   ∧ 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)