Theorem orim2d 795

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 793	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 715

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 716

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  796  orbi2d  797  pm2.82  819  stdcndcOLD  853  pm2.13dc  892  exmid1dc  4292  acexmidlemcase  6018  poxp  6402  fodjuomnilemdc  7348  omniwomnimkv  7371  exmidontriimlem1  7441  indpi  7567  suplocexprlemloc  7946  nneoor  9587  uzp1  9795  maxabslemlub  11790  xrmaxiflemlub  11831  nninfctlemfo  12634  exmidunben  13070  bj-nn0suc  16619  sbthomlem  16692