Theorem cliftetb

Description: show d is the same as an if-else involving a,b. (Contributed by Jarvin Udandy, 20-Sep-2020)

	Ref	Expression
Hypotheses	cliftetb.1	⊢ ( ( 𝜑 ∧ 𝜒 ) ∨ ( 𝜓 ∧ ¬ 𝜒 ) )
	cliftetb.2	⊢ 𝜃
Assertion	cliftetb	⊢ ( 𝜃 ↔ ( ( 𝜑 ∧ 𝜒 ) ∨ ( 𝜓 ∧ ¬ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		cliftetb.1	⊢ ( ( 𝜑 ∧ 𝜒 ) ∨ ( 𝜓 ∧ ¬ 𝜒 ) )
2		cliftetb.2	⊢ 𝜃
3	2 1	2th	⊢ ( 𝜃 ↔ ( ( 𝜑 ∧ 𝜒 ) ∨ ( 𝜓 ∧ ¬ 𝜒 ) ) )