Theorem orim2d 793

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 791	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 713

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 714

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  794  orbi2d  795  pm2.82  817  stdcndcOLD  851  pm2.13dc  890  exmid1dc  4288  acexmidlemcase  6008  poxp  6392  fodjuomnilemdc  7337  omniwomnimkv  7360  exmidontriimlem1  7429  indpi  7555  suplocexprlemloc  7934  nneoor  9575  uzp1  9783  maxabslemlub  11761  xrmaxiflemlub  11802  nninfctlemfo  12604  exmidunben  13040  bj-nn0suc  16509  sbthomlem  16579