This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem bianassc

Description: An inference to merge two lists of conjuncts. (Contributed by Peter Mazsa, 24-Sep-2022)

		Ref	Expression
	Hypothesis	bianass.1	$⊢ φ \leftrightarrow (ψ \land χ)$
	Assertion	bianassc	$⊢ (η \land φ) \leftrightarrow ((ψ \land η) \land χ)$

Step	Hyp	Ref	Expression
1		bianass.1	$⊢ φ \leftrightarrow (ψ \land χ)$
2	1	bianass	$⊢ (η \land φ) \leftrightarrow ((η \land ψ) \land χ)$
3		ancom	$⊢ (η \land ψ) \leftrightarrow (ψ \land η)$
4	2 3	bianbi	$⊢ (η \land φ) \leftrightarrow ((ψ \land η) \land χ)$