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Theorem jaao 530
 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 480 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 jaao.2 . . 3 (𝜃 → (𝜏𝜒))
43adantl 481 . 2 ((𝜑𝜃) → (𝜏𝜒))
52, 4jaod 394 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 382   ∧ wa 383 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 196  df-or 384  df-an 385 This theorem is referenced by:  pm3.44  532  pm3.48  874  prlem1  997  ordtri1  5673  ordun  5746  suc11  5748  funun  5846  poxp  7176  suc11reg  8399  rankunb  8596  gruun  9507  ofpreima2  28849  wl-orel12  32473  clsk1indlem3  37361
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