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))

Syntax hints:   → wi 4   ∨ wo 720

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 721

This theorem depends on definitions:  df-bi 117

This theorem is referenced 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  4341  exmidundifim  4342  exmid1stab  4343  elsuci  4546  acexmidlemcase  6074  undifdcss  7224  updjudhf  7413  ctssdccl  7445  zindd  9747  fiubm  11254  lswex  11339  fsumsplitsn  12160  fprodcllem  12356  fprodsplitsn  12383  gzsumwsubmcl  13784  gzsumwmhm  13786  subctctexmid  17013