Theorem orim1d 812

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
orim1d	⊢ (φ → ((ψ ∨ θ) → (χ ∨ θ)))

Proof of Theorem orim1d

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

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:  pm2.38  815  pm2.73  818  pm2.74  819  pm2.8  823  pm2.82  825  moeq3  3014  unss1  3433