Theorem orim1i 709

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 708	1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  19.34  1614  dveeq2or  1737  sbequilem  1759  sbequi  1760  dvelimALT  1927  dvelimfv  1928  dvelimor  1935  r19.45av  2514  acexmidlemcase  5527  nnm1nn0  8329