Theorem orim1i 761

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
orim1i	⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒))

Proof of Theorem orim1i

Step	Hyp	Ref	Expression
1		orim1i.1	. 2 ⊢ (𝜑 → 𝜓)
2		id 19	. 2 ⊢ (𝜒 → 𝜒)
3	1, 2	orim12i 760	1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ wo 709

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 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.34  1695  dveeq2or  1827  sbequilem  1849  sbequi  1850  dvelimALT  2022  dvelimfv  2023  dvelimor  2030  r19.45av  2650  acexmidlemcase  5891  omniwomnimkv  7195  nnm1nn0  9247  prmdc  12162  pcadd2  12373  triap  15236