Theorem orim1i 272

Description: Introduce disjunct to both sides of an implication.

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 9	. 2 ⊢ (χ → χ)
3	1, 2	orim12i 271	1 ⊢ ((φ ∨ χ) → (ψ ∨ χ))

Syntax hints:   → wi 2   ∨ wo 195

This theorem is referenced by:  pm2.85 439  19.34 772  r19.45av 1306

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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