Theorem orim2d 796

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 794	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 716

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 717

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  797  orbi2d  798  pm2.82  820  stdcndcOLD  854  pm2.13dc  893  exmid1dc  4319  acexmidlemcase  6054  poxp  6442  fodjuomnilemdc  7449  omniwomnimkv  7472  exmidontriimlem1  7542  indpi  7674  suplocexprlemloc  8053  nneoor  9702  uzp1  9910  maxabslemlub  11922  xrmaxiflemlub  11963  nninfctlemfo  12766  exmidunben  13266  bj-nn0suc  16875  sbthomlem  16946