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Theorem jaao 952
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 484 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 jaao.2 . . 3 (𝜃 → (𝜏𝜒))
43adantl 485 . 2 ((𝜑𝜃) → (𝜏𝜒))
52, 4jaod 856 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wo 844
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 210  df-an 400  df-or 845
This theorem is referenced by:  pm3.44  957  pm3.48  961  prlem1  1050  elpr2g  4552  ordtri1  6196  ordun  6264  suc11  6266  funun  6374  poxp  7809  suc11reg  9070  rankunb  9267  gruun  10221  ofpreima2  30432  wl-orel12  34909  clsk1indlem3  40733
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