Theorem orim12i 502

Description: Disjoin antecedents and consequents of two premises. (Contributed by NM, 6-Jun-1994.) (Proof shortened by Wolf Lammen, 25-Jul-2012.)

Hypotheses

Ref	Expression
orim12i.1	⊢ (φ → ψ)
orim12i.2	⊢ (χ → θ)

Assertion

Ref	Expression
orim12i	⊢ ((φ ∨ χ) → (ψ ∨ θ))

Proof of Theorem orim12i

Step	Hyp	Ref	Expression
1		orim12i.1	. . 3 ⊢ (φ → ψ)
2	1	orcd 381	. 2 ⊢ (φ → (ψ ∨ θ))
3		orim12i.2	. . 3 ⊢ (χ → θ)
4	3	olcd 382	. 2 ⊢ (χ → (ψ ∨ θ))
5	2, 4	jaoi 368	1 ⊢ ((φ ∨ χ) → (ψ ∨ θ))

This proof depends on syntax axioms:   → wi 4   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  orim1i  503  orim2i  504  prlem2  929  eueq3  3012  lefinlteq  4464  funcnvuni  5162  muc0or  6253  nchoicelem9  6298