Theorem pm3.44 497

Description: Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)

Assertion

Ref	Expression
pm3.44	⊢ (((ψ → φ) ∧ (χ → φ)) → ((ψ ∨ χ) → φ))

Proof of Theorem pm3.44

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((ψ → φ) → (ψ → φ))
2		id 19	. 2 ⊢ ((χ → φ) → (χ → φ))
3	1, 2	jaao 495	1 ⊢ (((ψ → φ) ∧ (χ → φ)) → ((ψ ∨ χ) → φ))

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:  jao  498  jaob  758