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Theorem jaao 940
Description: Inference conjoining and disjoining the antecedents of two implications. (Contributed by NM, 30-Sep-1999.)
Hypotheses
Ref Expression
jaao.1 (𝜑 → (𝜓𝜒))
jaao.2 (𝜃 → (𝜏𝜒))
Assertion
Ref Expression
jaao ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))

Proof of Theorem jaao
StepHypRef Expression
1 jaao.1 . . 3 (𝜑 → (𝜓𝜒))
21adantr 474 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 jaao.2 . . 3 (𝜃 → (𝜏𝜒))
43adantl 475 . 2 ((𝜑𝜃) → (𝜏𝜒))
52, 4jaod 848 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386  wo 836
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 199  df-an 387  df-or 837
This theorem is referenced by:  pm3.44  945  pm3.48  949  prlem1  1038  ordtri1  6009  ordun  6077  suc11  6079  funun  6180  poxp  7570  suc11reg  8813  rankunb  9010  gruun  9963  ofpreima2  30031  wl-orel12  33889  clsk1indlem3  39297
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