Theorem orim2d 788

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 786	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 708

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 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  789  orbi2d  790  pm2.82  812  stdcndcOLD  846  pm2.13dc  885  exmid1dc  4200  acexmidlemcase  5869  poxp  6232  fodjuomnilemdc  7141  omniwomnimkv  7164  exmidontriimlem1  7219  indpi  7340  suplocexprlemloc  7719  nneoor  9354  uzp1  9560  maxabslemlub  11215  xrmaxiflemlub  11255  exmidunben  12426  bj-nn0suc  14686  sbthomlem  14743