Theorem orim2d 438

Description: Disjoin antecedents and consequents in a deduction.

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 11	. 2 ⊢ (φ → (θ → θ))
2		orim1d.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	orim12d 436	1 ⊢ (φ → ((θ ∨ ψ) → (θ ∨ χ)))

Syntax hints:   → wi 2   ∨ wo 195

This theorem is referenced by:  nneo 4719

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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