Theorem orim2d 795

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 793	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 715

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 716

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  796  orbi2d  797  pm2.82  819  stdcndcOLD  853  pm2.13dc  892  exmid1dc  4290  acexmidlemcase  6013  poxp  6397  fodjuomnilemdc  7343  omniwomnimkv  7366  exmidontriimlem1  7436  indpi  7562  suplocexprlemloc  7941  nneoor  9582  uzp1  9790  maxabslemlub  11769  xrmaxiflemlub  11810  nninfctlemfo  12613  exmidunben  13049  bj-nn0suc  16580  sbthomlem  16650