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Theorem jaao 953
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 481 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 jaao.2 . . 3 (𝜃 → (𝜏𝜒))
43adantl 482 . 2 ((𝜑𝜃) → (𝜏𝜒))
52, 4jaod 857 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wo 845
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 206  df-an 397  df-or 846
This theorem is referenced by:  pm3.44  958  pm3.48  962  prlem1  1053  elpr2g  4610  ordtri1  6350  ordun  6421  suc11  6424  funun  6547  poxp  8059  suc11reg  9554  rankunb  9785  gruun  10741  ofpreima2  31580  wl-orel12  35961  clsk1indlem3  42297
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