Theorem pm3.44 974

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 23	. 2 ⊢ ((𝜓 → 𝜑) → (𝜓 → 𝜑))
2		id 23	. 2 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜑))
3	1, 2	jaao 969	1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) → ((𝜓 ∨ 𝜒) → 𝜑))

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:  jao  975  jaob  976  ssfi  9172  dvmptconst  46869  dvmptidg  46871  dvmulcncf  46879  dvdivcncf  46881  fourierdlem101  47161