Theorem orim2d 788

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 786	1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 708

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 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  789  orbi2d  790  pm2.82  812  stdcndcOLD  846  pm2.13dc  885  exmid1dc  4201  acexmidlemcase  5870  poxp  6233  fodjuomnilemdc  7142  omniwomnimkv  7165  exmidontriimlem1  7220  indpi  7341  suplocexprlemloc  7720  nneoor  9355  uzp1  9561  maxabslemlub  11216  xrmaxiflemlub  11256  exmidunben  12427  bj-nn0suc  14719  sbthomlem  14776