Theorem orim2d 789

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 787	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 709

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 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  790  orbi2d  791  pm2.82  813  stdcndcOLD  847  pm2.13dc  886  exmid1dc  4230  acexmidlemcase  5914  poxp  6287  fodjuomnilemdc  7205  omniwomnimkv  7228  exmidontriimlem1  7283  indpi  7404  suplocexprlemloc  7783  nneoor  9422  uzp1  9629  maxabslemlub  11354  xrmaxiflemlub  11394  nninfctlemfo  12180  exmidunben  12586  bj-nn0suc  15526  sbthomlem  15585