Theorem orim1i 922

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 23	. 2 ⊢ (𝜒 → 𝜒)
3	1, 2	orim12i 921	1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ wo 860

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-or 861

This theorem is referenced by:  19.34  2015  r19.45v  3199  nnm1nn0  12536  elfzo0l  13776  xrge0iifhom  34244  fmla1  35750  bj-andnotim  37043  orfa2  38597  expdioph  43612  ifpimim  44097  simpcntrab  47442