Theorem orim1d 967

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
orim1d	⊢ (𝜑 → ((𝜓 ∨ 𝜃) → (𝜒 ∨ 𝜃)))

Proof of Theorem orim1d

Step	Hyp	Ref	Expression
1		orim1d.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		idd 24	. 2 ⊢ (𝜑 → (𝜃 → 𝜃))
3	1, 2	orim12d 966	1 ⊢ (𝜑 → ((𝜓 ∨ 𝜃) → (𝜒 ∨ 𝜃)))

Syntax hints:   → 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:  pm2.38  970  pm2.8  974  pm2.73  975  pm2.74  976  pm2.82  977  moeq3  3720  unss1  4194  ordtri2or2  6484  gchor  10664  relin01  11784  icombl  25612  ioombl  25613  coltr  28669  frgrregorufrg  30354  cycpmco2  33135  fmlasuc  35370  satffunlem1lem2  35387  satffunlem2lem2  35390  naim1  36371  onsucconni  36419  dnibndlem13  36472  mblfinlem2  37644  leat3  39276  meetat2  39278  paddss1  39799  onov0suclim  43263  dflim5  43318  ordsssucim  43391