Theorem joinimandres3-P4.RC 583

Description: Inference Form of joinimandres3-P4 582. †

Hypotheses

Ref	Expression
joinimandres3-P4.RC.1	⊢ (𝜑 → 𝜓)
joinimandres3-P4.RC.2	⊢ (𝜑 → 𝜒)

Assertion

Ref	Expression
joinimandres3-P4.RC	⊢ (𝜑 → (𝜓 ∧ 𝜒))

Proof of Theorem joinimandres3-P4.RC

Step	Hyp	Ref	Expression
1		joinimandres3-P4.RC.1	. . . 4 ⊢ (𝜑 → 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → 𝜓))
3		joinimandres3-P4.RC.2	. . . 4 ⊢ (𝜑 → 𝜒)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → 𝜒))
5	2, 4	joinimandres3-P4 582	. 2 ⊢ (⊤ → (𝜑 → (𝜓 ∧ 𝜒)))
6	5	ndtruee-P3.18 183	1 ⊢ (𝜑 → (𝜓 ∧ 𝜒))

Syntax hints:   → wff-imp 10   ∧ 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)