Theorem olcd 382

Description: Deduction introducing a disjunct. A translation of natural deduction rule ∨ IL ( ∨ insertion left), see natded in set.mm. (Contributed by NM, 11-Apr-2008.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)

Hypothesis

Ref	Expression
orcd.1	⊢ (φ → ψ)

Assertion

Ref	Expression
olcd	⊢ (φ → (χ ∨ ψ))

Proof of Theorem olcd

Step	Hyp	Ref	Expression
1		orcd.1	. . 3 ⊢ (φ → ψ)
2	1	orcd 381	. 2 ⊢ (φ → (ψ ∨ χ))
3	2	orcomd 377	1 ⊢ (φ → (χ ∨ ψ))

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

This theorem is referenced by:  pm2.48  389  pm2.49  390  orim12i  502  pm1.5  508  nnc0suc  4413  clos1basesuc  5883  nc0le1  6217  frecsuc  6323