Theorem orim2d 790

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 788	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 710

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 711

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  791  orbi2d  792  pm2.82  814  stdcndcOLD  848  pm2.13dc  887  exmid1dc  4248  acexmidlemcase  5946  poxp  6325  fodjuomnilemdc  7253  omniwomnimkv  7276  exmidontriimlem1  7340  indpi  7462  suplocexprlemloc  7841  nneoor  9482  uzp1  9689  maxabslemlub  11562  xrmaxiflemlub  11603  nninfctlemfo  12405  exmidunben  12841  bj-nn0suc  15974  sbthomlem  16038