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Theorem jaao 531
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 395 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 383  wa 384
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 197  df-or 385  df-an 386
This theorem is referenced by:  pm3.44  533  pm3.48  878  prlem1  1005  ordtri1  5754  ordun  5827  suc11  5829  funun  5930  poxp  7286  suc11reg  8513  rankunb  8710  gruun  9625  ofpreima2  29451  wl-orel12  33274  clsk1indlem3  38167
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