Theorem bianass

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

	Ref	Expression
Hypothesis	bianass.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
Assertion	bianass	⊢ ( ( 𝜂 ∧ 𝜑 ) ↔ ( ( 𝜂 ∧ 𝜓 ) ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		bianass.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
2	1	anbi2i	⊢ ( ( 𝜂 ∧ 𝜑 ) ↔ ( 𝜂 ∧ ( 𝜓 ∧ 𝜒 ) ) )
3		anass	⊢ ( ( ( 𝜂 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( 𝜂 ∧ ( 𝜓 ∧ 𝜒 ) ) )
4	2 3	bitr4i	⊢ ( ( 𝜂 ∧ 𝜑 ) ↔ ( ( 𝜂 ∧ 𝜓 ) ∧ 𝜒 ) )