Theorem biancomd

Description: Commuting conjunction in a biconditional, deduction form. (Contributed by Peter Mazsa, 3-Oct-2018)

	Ref	Expression
Hypothesis	biancomd.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜃 ∧ 𝜒 ) ) )
Assertion	biancomd	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ∧ 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		biancomd.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜃 ∧ 𝜒 ) ) )
2		ancom	⊢ ( ( 𝜃 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜃 ) )
3	1 2	bitrdi	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ∧ 𝜃 ) ) )