Theorem orim2d 796

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 794	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 716

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 717

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  797  orbi2d  798  pm2.82  820  stdcndcOLD  854  pm2.13dc  893  exmid1dc  4315  acexmidlemcase  6047  poxp  6430  fodjuomnilemdc  7437  omniwomnimkv  7460  exmidontriimlem1  7530  indpi  7662  suplocexprlemloc  8041  nneoor  9686  uzp1  9894  maxabslemlub  11900  xrmaxiflemlub  11941  nninfctlemfo  12744  exmidunben  13198  bj-nn0suc  16783  sbthomlem  16854