Theorem orim2i 773

Description: Introduce disjunct to both sides of an implication. (Contributed by NM, 6-Jun-1994.)

Hypothesis

Ref	Expression
orim1i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
orim2i	⊢ ((𝜒 ∨ 𝜑) → (𝜒 ∨ 𝜓))

Proof of Theorem orim2i

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝜒 → 𝜒)
2		orim1i.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	orim12i 771	1 ⊢ ((𝜒 ∨ 𝜑) → (𝜒 ∨ 𝜓))

This proof depends on syntax axioms:   → wi 4   ∨ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  orbi2i  774  pm1.5  777  pm2.3  787  ordi  828  dcn  854  pm2.25dc  905  dcand  945  axi12  1567  dveeq2or  1869  equs5or  1883  sb4or  1886  sb4bor  1888  nfsb2or  1890  sbequilem  1891  sbequi  1892  sbal1yz  2061  dvelimor  2078  exmodc  2137  r19.44av  2710  exmidundif  4343  exmidundifim  4344  exmid1stab  4345  elsuci  4548  acexmidlemcase  6080  undifdcss  7230  updjudhf  7420  ctssdccl  7452  zindd  9769  fiubm  11286  lswex  11371  fsumsplitsn  12195  fprodcllem  12391  fprodsplitsn  12418  gzsumwsubmcl  13852  gzsumwmhm  13854  subctctexmid  17152