Theorem dedtOLD 1028

Description: Old version of dedt 1025. Obsolete as of 16-Mar-2021. (Contributed by NM, 26-Jun-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
dedtOLD.1	⊢ ((𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜃 ↔ 𝜏))
dedtOLD.2	⊢ 𝜏

Assertion

Ref	Expression
dedtOLD	⊢ (𝜒 → 𝜃)

Proof of Theorem dedtOLD

Step	Hyp	Ref	Expression
1		dedlema 993	. 2 ⊢ (𝜒 → (𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))))
2		dedtOLD.2	. . 3 ⊢ 𝜏
3		dedtOLD.1	. . 3 ⊢ ((𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜃 ↔ 𝜏))
4	2, 3	mpbiri 247	. 2 ⊢ ((𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → 𝜃)
5	1, 4	syl 17	1 ⊢ (𝜒 → 𝜃)

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 195   ∨ wo 382   ∧ wa 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385

This theorem is referenced by:  con3OLD  1029