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Theorem jaoian 784
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 114 . . 3 (𝜑 → (𝜓𝜒))
3 jaoian.2 . . . 4 ((𝜃𝜓) → 𝜒)
43ex 114 . . 3 (𝜃 → (𝜓𝜒))
52, 4jaoi 705 . 2 ((𝜑𝜃) → (𝜓𝜒))
65imp 123 1 (((𝜑𝜃) ∧ 𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ordi  805  ccase  948  xaddnemnf  9633  xaddnepnf  9634  faclbnd  10480  faclbnd3  10482
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