Theorem pm3.48 806

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 374	. . 3 ⊢ (ψ → (ψ ∨ θ))
2	1	imim2i 13	. 2 ⊢ ((φ → ψ) → (φ → (ψ ∨ θ)))
3		olc 373	. . 3 ⊢ (θ → (ψ ∨ θ))
4	3	imim2i 13	. 2 ⊢ ((χ → θ) → (χ → (ψ ∨ θ)))
5	2, 4	jaao 495	1 ⊢ (((φ → ψ) ∧ (χ → θ)) → ((φ ∨ χ) → (ψ ∨ θ)))

Syntax hints:   → wi 4   ∨ wo 357   ∧ wa 358

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  df-an 360

This theorem is referenced by:  orim12d  811