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Theorem jaoian 959
Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005.)
Hypotheses
Ref Expression
jaoian.1 ((𝜑𝜓) → 𝜒)
jaoian.2 ((𝜃𝜓) → 𝜒)
Assertion
Ref Expression
jaoian (((𝜑𝜃) ∧ 𝜓) → 𝜒)

Proof of Theorem jaoian
StepHypRef Expression
1 jaoian.1 . . . 4 ((𝜑𝜓) → 𝜒)
21ex 412 . . 3 (𝜑 → (𝜓𝜒))
3 jaoian.2 . . . 4 ((𝜃𝜓) → 𝜒)
43ex 412 . . 3 (𝜃 → (𝜓𝜒))
52, 4jaoi 858 . 2 ((𝜑𝜃) → (𝜓𝜒))
65imp 406 1 (((𝜑𝜃) ∧ 𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  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:  ccase  1038  preq12nebg  4863  opthprneg  4865  elpreqpr  4867  tpres  7221  xaddnemnf  13278  xaddnepnf  13279  faclbnd  14329  faclbnd3  14331  faclbnd4lem1  14332  znf1o  21570  degltlem1  26111  ipasslem3  30852  padct  32731  fz1nntr  32806  xrge0iifhom  33936  bj-ideqg1ALT  37166  nn0addcom  42480  nn0mulcom  42484  fzsplit1nn0  42765  f1mo  48762
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