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  4234  acexmidlemcase  5920  poxp  6294  fodjuomnilemdc  7214  omniwomnimkv  7237  exmidontriimlem1  7293  indpi  7414  suplocexprlemloc  7793  nneoor  9433  uzp1  9640  maxabslemlub  11377  xrmaxiflemlub  11418  nninfctlemfo  12220  exmidunben  12656  bj-nn0suc  15657  sbthomlem  15719