Theorem orim1i 923

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 922	1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒))

This proof depends on syntax axioms:   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  19.34  2025  r19.45v  3202  nnm1nn0  12563  elfzo0l  13804  xrge0iifhom  34358  fmla1  35900  bj-andnotim  37222  orfa2  38778  expdioph  43791  ifpimim  44276  simpcntrab  47625