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Theorem jaao 954
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 482 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 jaao.2 . . 3 (𝜃 → (𝜏𝜒))
43adantl 483 . 2 ((𝜑𝜃) → (𝜏𝜒))
52, 4jaod 858 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  wo 846
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 398  df-or 847
This theorem is referenced by:  pm3.44  959  pm3.48  963  prlem1  1054  elpr2g  4615  ordtri1  6355  ordun  6426  suc11  6429  funun  6552  poxp  8065  suc11reg  9562  rankunb  9793  gruun  10749  ofpreima2  31624  wl-orel12  35999  clsk1indlem3  42389
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