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Metamath Proof Explorer

Theorem bianass

Description: An inference to merge two lists of conjuncts. (Contributed by Giovanni Mascellani, 23-May-2019)

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

Step	Hyp	Ref	Expression
1		bianass.1	$⊢ φ \leftrightarrow (ψ \land χ)$
2	1	anbi2i	$⊢ (η \land φ) \leftrightarrow (η \land (ψ \land χ))$
3		anass	$⊢ ((η \land ψ) \land χ) \leftrightarrow (η \land (ψ \land χ))$
4	2 3	bitr4i	$⊢ (η \land φ) \leftrightarrow ((η \land ψ) \land χ)$