Theorem orim2d 800

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
orim2d	⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (𝜑 → (𝜃 → 𝜃))
2		orim1d.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	orim12d 798	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 720

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  801  orbi2d  802  pm2.82  824  stdcndcOLD  858  pm2.13dc  897  exmid1dc  4335  acexmidlemcase  6074  poxp  6462  fodjuomnilemdc  7478  omniwomnimkv  7501  exmidontriimlem1  7571  indpi  7703  suplocexprlemloc  8082  nneoor  9731  uzp1  9939  maxabslemlub  11956  xrmaxiflemlub  11997  nninfctlemfo  12800  exmidunben  13300  bj-nn0suc  16973  sbthomlem  17044