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Theorem 3jaoi 1235
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 1117 . 2 ((𝜑𝜓) ∧ (𝜒𝜓) ∧ (𝜃𝜓))
5 3jao 1233 . 2 (((𝜑𝜓) ∧ (𝜒𝜓) ∧ (𝜃𝜓)) → ((𝜑𝜒𝜃) → 𝜓))
64, 5ax-mp 7 1 ((𝜑𝜒𝜃) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  w3o 919  w3a 920
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 921  df-3an 922
This theorem is referenced by:  3jaoian  1237  3ianorr  1241  acexmidlem1  5539  nndceq  6143  nndcel  6144  znegcl  8463  xrltnr  8931  nltpnft  8960  ngtmnft  8961  xrrebnd  8962  xnegcl  8975  xnegneg  8976  xltnegi  8978
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