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  4285  acexmidlemcase  6005  poxp  6389  fodjuomnilemdc  7327  omniwomnimkv  7350  exmidontriimlem1  7419  indpi  7545  suplocexprlemloc  7924  nneoor  9565  uzp1  9773  maxabslemlub  11739  xrmaxiflemlub  11780  nninfctlemfo  12582  exmidunben  13018  bj-nn0suc  16436  sbthomlem  16507