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Theorem 3jaoi 1237
Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)
Hypotheses
Ref Expression
3jaoi.1 (𝜑𝜓)
3jaoi.2 (𝜒𝜓)
3jaoi.3 (𝜃𝜓)
Assertion
Ref Expression
3jaoi ((𝜑𝜒𝜃) → 𝜓)

Proof of Theorem 3jaoi
StepHypRef Expression
1 3jaoi.1 . . 3 (𝜑𝜓)
2 3jaoi.2 . . 3 (𝜒𝜓)
3 3jaoi.3 . . 3 (𝜃𝜓)
41, 2, 33pm3.2i 1119 . 2 ((𝜑𝜓) ∧ (𝜒𝜓) ∧ (𝜃𝜓))
5 3jao 1235 . 2 (((𝜑𝜓) ∧ (𝜒𝜓) ∧ (𝜃𝜓)) → ((𝜑𝜒𝜃) → 𝜓))
64, 5ax-mp 7 1 ((𝜑𝜒𝜃) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  w3o 921  w3a 922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115  df-3or 923  df-3an 924
This theorem is referenced by:  3jaoian  1239  3ianorr  1243  acexmidlem1  5611  nndceq  6216  nndcel  6217  znegcl  8717  xrltnr  9185  nltpnft  9214  ngtmnft  9215  xrrebnd  9216  xnegcl  9229  xnegneg  9230  xltnegi  9232
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