Theorem orcd 381

Description: Deduction introducing a disjunct. A translation of natural deduction rule ∨ IR ( ∨ insertion right), see natded in set.mm. (Contributed by NM, 20-Sep-2007.)

Hypothesis

Ref	Expression
orcd.1	⊢ (φ → ψ)

Assertion

Ref	Expression
orcd	⊢ (φ → (ψ ∨ χ))

Proof of Theorem orcd

Step	Hyp	Ref	Expression
1		orcd.1	. 2 ⊢ (φ → ψ)
2		orc 374	. 2 ⊢ (ψ → (ψ ∨ χ))
3	1, 2	syl 15	1 ⊢ (φ → (ψ ∨ 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

This theorem is referenced by:  olcd  382  pm2.47  388  orim12i  502  sbc2or  3055  undif3  3516  nc0le1  6217  dmfrec  6317  frec0  6322