Theorem an12i 36183

Description: An inference from commuting operands in a chain of conjunctions. (Contributed by Giovanni Mascellani, 22-May-2019.)

Hypothesis

Ref	Expression
an12i.1	⊢ (𝜑 ∧ (𝜓 ∧ 𝜒))

Assertion

Ref	Expression
an12i	⊢ (𝜓 ∧ (𝜑 ∧ 𝜒))

Proof of Theorem an12i

Step	Hyp	Ref	Expression
1		an12i.1	. 2 ⊢ (𝜑 ∧ (𝜓 ∧ 𝜒))
2		an12 641	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒)))
3	1, 2	mpbir 230	1 ⊢ (𝜓 ∧ (𝜑 ∧ 𝜒))

Syntax hints:   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396

This theorem is referenced by: (None)