Theorem 3ancomb 589

Description: Commutation law for triple conjunction.

Assertion

Ref	Expression
3ancomb	⊢ ((φ ∧ ψ ∧ χ) ↔ (φ ∧ χ ∧ ψ))

Proof of Theorem 3ancomb

Step	Hyp	Ref	Expression
1		3ancoma 588	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (ψ ∧ φ ∧ χ))
2		3anrot 586	. 2 ⊢ ((ψ ∧ φ ∧ χ) ↔ (φ ∧ χ ∧ ψ))
3	1, 2	bitr 151	1 ⊢ ((φ ∧ ψ ∧ χ) ↔ (φ ∧ χ ∧ ψ))

Syntax hints:   ↔ wb 127   ∧ w3a 581

This theorem is referenced by:  3simpb 592

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

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