Theorem cnfn1dd 38100

Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)

Hypotheses

Ref	Expression
cnfn1dd.1	⊢ (𝜑 → (𝜓 → 𝜒))
cnfn1dd.2	⊢ (𝜑 → (𝜓 → (¬ 𝜒 ∨ 𝜃)))

Assertion

Ref	Expression
cnfn1dd	⊢ (𝜑 → (𝜓 → 𝜃))

Proof of Theorem cnfn1dd

Step	Hyp	Ref	Expression
1		cnfn1dd.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2		notnot 142	. . 3 ⊢ (𝜒 → ¬ ¬ 𝜒)
3	1, 2	syl6 35	. 2 ⊢ (𝜑 → (𝜓 → ¬ ¬ 𝜒))
4		cnfn1dd.2	. 2 ⊢ (𝜑 → (𝜓 → (¬ 𝜒 ∨ 𝜃)))
5	3, 4	cnf1dd 38098	1 ⊢ (𝜑 → (𝜓 → 𝜃))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 847

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 207  df-an 396  df-or 848

This theorem is referenced by:  mpobi123f  38170  mptbi12f  38174  ac6s6  38180