Theorem biimpor

Description: A rewriting rule for biconditional. (Contributed by Giovanni Mascellani, 15-Sep-2017)

	Ref	Expression
Assertion	biimpor	⊢ ( ( ( 𝜑 ↔ 𝜓 ) → 𝜒 ) ↔ ( ( ¬ 𝜑 ↔ 𝜓 ) ∨ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		imor	⊢ ( ( ( 𝜑 ↔ 𝜓 ) → 𝜒 ) ↔ ( ¬ ( 𝜑 ↔ 𝜓 ) ∨ 𝜒 ) )
2		notbinot2	⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) ↔ ( ¬ 𝜑 ↔ 𝜓 ) )
3	2	orbi1i	⊢ ( ( ¬ ( 𝜑 ↔ 𝜓 ) ∨ 𝜒 ) ↔ ( ( ¬ 𝜑 ↔ 𝜓 ) ∨ 𝜒 ) )
4	1 3	bitri	⊢ ( ( ( 𝜑 ↔ 𝜓 ) → 𝜒 ) ↔ ( ( ¬ 𝜑 ↔ 𝜓 ) ∨ 𝜒 ) )