Theorem jao 963

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		pm3.44 962	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜓)) → ((𝜑 ∨ 𝜒) → 𝜓))
2	1	ex 412	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜓) → ((𝜑 ∨ 𝜒) → 𝜓)))

Syntax hints:   → wi 4   ∨ wo 848

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 207  df-an 396  df-or 849

This theorem is referenced by:  3jao  1428  en3lplem2  9534  indpi  10830  bj-orim2  36777  jaodd  42572  jaoded  44916  suctrALT2VD  45185  suctrALT2  45186  en3lplem2VD  45193  hbimpgVD  45253  ax6e2ndeqVD  45258  suctrALTcf  45271  suctrALTcfVD  45272  ax6e2ndeqALT  45280