Theorem orcnd 878

Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Hypotheses

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

Assertion

Ref	Expression
orcnd	⊢ (𝜑 → 𝜒)

Proof of Theorem orcnd

Step	Hyp	Ref	Expression
1		orcnd.1	. . 3 ⊢ (𝜑 → (𝜓 ∨ 𝜒))
2	1	orcomd 871	. 2 ⊢ (𝜑 → (𝜒 ∨ 𝜓))
3		orcnd.2	. 2 ⊢ (𝜑 → ¬ 𝜓)
4	2, 3	olcnd 877	1 ⊢ (𝜑 → 𝜒)

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-or 848

This theorem is referenced by:  poxp2  8125  poxp3  8132  nnaordex2  8606  fpwwe2lem12  10602  evlslem3  21994  psdmul  22060  fzone1  32730  ccatws1f1o  32880  chnub  32945  0ringsubrg  33209  drngidl  33411  mxidlmaxv  33446  mxidlprm  33448  rprmasso2  33504  1arithidom  33515  zringidom  33529  fldext2chn  33725  aks6d1c2p2  42114  aks6d1c5  42134