Theorem pm3.44 532

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 22	. 2 ⊢ ((𝜓 → 𝜑) → (𝜓 → 𝜑))
2		id 22	. 2 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜑))
3	1, 2	jaao 530	1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑))

Syntax hints:   → wi 4   ∨ wo 382   ∧ wa 383

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 196  df-or 384  df-an 385

This theorem is referenced by:  jao  533  jaob  818  dvmptconst  38803  dvmptidg  38805  dvmulcncf  38815  dvdivcncf  38817  fourierdlem101  39100