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  4312  acexmidlemcase  6044  poxp  6427  fodjuomnilemdc  7434  omniwomnimkv  7457  exmidontriimlem1  7527  indpi  7653  suplocexprlemloc  8032  nneoor  9676  uzp1  9884  maxabslemlub  11885  xrmaxiflemlub  11926  nninfctlemfo  12729  exmidunben  13166  bj-nn0suc  16721  sbthomlem  16792