Theorem orim1i 503

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 502	1 ⊢ ((φ ∨ χ) → (ψ ∨ χ))

Syntax hints:   → wi 4   ∨ wo 357

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 177  df-or 359

This theorem is referenced by:  19.34  1663  r19.45av  2769  leconnnc  6219