Theorem olci 227

Description: Deduction eliminating disjunct.

Hypothesis

Ref	Expression
olci.1	⊢ ((φ ∨ ψ) → χ)

Assertion

Ref	Expression
olci	⊢ (ψ → χ)

Proof of Theorem olci

Step	Hyp	Ref	Expression
1		olc 224	. 2 ⊢ (ψ → (φ ∨ ψ))
2		olci.1	. 2 ⊢ ((φ ∨ ψ) → χ)
3	1, 2	syl 12	1 ⊢ (ψ → χ)

Syntax hints:   → wi 2   ∨ wo 195

This theorem is referenced by:  eueq3 1430  sucid 2304

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

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