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)))

This proof depends on syntax axioms:   → wi 4   ∨ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  orim2  801  orbi2d  802  pm2.82  824  stdcndcOLD  858  pm2.13dc  897  exmid1dc  4339  acexmidlemcase  6083  poxp  6472  fodjuomnilemdc  7491  omniwomnimkv  7514  exmidontriimlem1  7584  indpi  7716  suplocexprlemloc  8095  nneoor  9760  uzp1  9973  maxabslemlub  11997  xrmaxiflemlub  12040  nninfctlemfo  12843  exmidunben  13376  bj-nn0suc  17207  sbthomlem  17288