Theorem jao 973

Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)

Assertion

Ref	Expression
jao	⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((𝜑 ∨ 𝜒) → 𝜓)))

Proof of Theorem jao

Step	Hyp	Ref	Expression
1		pm3.44 972	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)) → ((𝜑 ∨ 𝜒) → 𝜓))
2	1	ex 416	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((𝜑 ∨ 𝜒) → 𝜓)))

Syntax hints:   → wi 4   ∨ wo 858

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 209  df-an 400  df-or 859

This theorem is referenced by:  3jao  1443  en3lplem2  9565  indpi  10862  axtco2  36798  bj-orim2  36962  jaodd  42789  jaoded  45106  suctrALT2VD  45375  suctrALT2  45376  en3lplem2VD  45383  hbimpgVD  45443  ax6e2ndeqVD  45448  suctrALTcf  45461  suctrALTcfVD  45462  ax6e2ndeqALT  45470