Theorem andassoc2b-P4 570

Description: Alternate Form B of andassoc-P3.36 317. †

Hypothesis

Ref	Expression
andassoc2b-P4.1	⊢ (𝛾 → (𝜑 ∧ (𝜓 ∧ 𝜒)))

Assertion

Ref	Expression
andassoc2b-P4	⊢ (𝛾 → ((𝜑 ∧ 𝜓) ∧ 𝜒))

Proof of Theorem andassoc2b-P4

Step	Hyp	Ref	Expression
1		andassoc2b-P4.1	. 2 ⊢ (𝛾 → (𝜑 ∧ (𝜓 ∧ 𝜒)))
2		andassoc-P3.36 317	. . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))
3	2	bisym-P3.33b.RC 299	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
4	1, 3	subimr2-P4.RC 543	1 ⊢ (𝛾 → ((𝜑 ∧ 𝜓) ∧ 𝜒))

Syntax hints:   → wff-imp 10   ∧ wff-and 132

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:  andassoc2b-P4.RC  571