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  4284  acexmidlemcase  6002  poxp  6384  fodjuomnilemdc  7319  omniwomnimkv  7342  exmidontriimlem1  7411  indpi  7537  suplocexprlemloc  7916  nneoor  9557  uzp1  9764  maxabslemlub  11726  xrmaxiflemlub  11767  nninfctlemfo  12569  exmidunben  13005  bj-nn0suc  16351  sbthomlem  16423