Theorem orim2d 813

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
orim2d	⊢ (φ → ((θ ∨ ψ) → (θ ∨ χ)))

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (φ → (θ → θ))
2		orim1d.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	orim12d 811	1 ⊢ (φ → ((θ ∨ ψ) → (θ ∨ 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  df-an 360

This theorem is referenced by:  orim2  814  pm2.82  825