Theorem orim2d 792

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 790	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 712

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 713

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  793  orbi2d  794  pm2.82  816  stdcndcOLD  850  pm2.13dc  889  exmid1dc  4263  acexmidlemcase  5969  poxp  6348  fodjuomnilemdc  7279  omniwomnimkv  7302  exmidontriimlem1  7371  indpi  7497  suplocexprlemloc  7876  nneoor  9517  uzp1  9724  maxabslemlub  11684  xrmaxiflemlub  11725  nninfctlemfo  12527  exmidunben  12963  bj-nn0suc  16237  sbthomlem  16304