Theorem pm3.48 978

Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.)

Assertion

Ref	Expression
pm3.48	⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃)))

Proof of Theorem pm3.48

Step	Hyp	Ref	Expression
1		orc 881	. . 3 ⊢ (𝜓 → (𝜓 ∨ 𝜃))
2	1	imim2i 17	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∨ 𝜃)))
3		olc 882	. . 3 ⊢ (𝜃 → (𝜓 ∨ 𝜃))
4	3	imim2i 17	. 2 ⊢ ((𝜒 → 𝜃) → (𝜒 → (𝜓 ∨ 𝜃)))
5	2, 4	jaao 969	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜃)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∨ wo 861

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

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by:  orim12d  979  tz7.48lem  8430  caubnd  15430  bj-nnfor  37414