Theorem 3jcadALT 36421

Description: Alternate proof of 3jcad 1147. (Contributed by Hongxiu Chen, 29-Jun-2025.) (Proof modification is discouraged.) Use 3jcad instead. (New usage is discouraged.)

Hypotheses

Ref	Expression
3jcadALT.1	⊢ (𝜑 → (𝜓 → 𝜒))
3jcadALT.2	⊢ (𝜑 → (𝜓 → 𝜃))
3jcadALT.3	⊢ (𝜑 → (𝜓 → 𝜏))

Assertion

Ref	Expression
3jcadALT	⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃 ∧ 𝜏)))

Proof of Theorem 3jcadALT

Step	Hyp	Ref	Expression
1		3jcadALT.1	. . . 4 ⊢ (𝜑 → (𝜓 → 𝜒))
2		3jcadALT.2	. . . 4 ⊢ (𝜑 → (𝜓 → 𝜃))
3	1, 2	jcad 522	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃)))
4		3jcadALT.3	. . 3 ⊢ (𝜑 → (𝜓 → 𝜏))
5	3, 4	jcad 522	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) ∧ 𝜏)))
6		df-3an 1105	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜏) ↔ ((𝜒 ∧ 𝜃) ∧ 𝜏))
7	5, 6	imbitrrdi 255	1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃 ∧ 𝜏)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by: (None)