Theorem bibi1i

Description: Inference adding a biconditional to the right in an equivalence. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypothesis	bibi2i.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	bibi1i	⊢ ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		bibi2i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		bicom	⊢ ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜒 ↔ 𝜑 ) )
3	1	bibi2i	⊢ ( ( 𝜒 ↔ 𝜑 ) ↔ ( 𝜒 ↔ 𝜓 ) )
4		bicom	⊢ ( ( 𝜒 ↔ 𝜓 ) ↔ ( 𝜓 ↔ 𝜒 ) )
5	2 3 4	3bitri	⊢ ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜒 ) )