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Theorem 3expib 1167
 Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3expib (𝜑 → ((𝜓𝜒) → 𝜃))

Proof of Theorem 3expib
StepHypRef Expression
1 3exp.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213exp 1163 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32impd 252 1 (𝜑 → ((𝜓𝜒) → 𝜃))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 945 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107 This theorem depends on definitions:  df-bi 116  df-3an 947 This theorem is referenced by:  3anidm12  1256  mob  2837  eqbrrdva  4677  funimaexglem  5174  fco  5256  f1oiso2  5694  caovimo  5930  smoel2  6166  nnaword  6373  3ecoptocl  6484  sbthlemi10  6820  distrnq0  7231  addassnq0  7234  prcdnql  7256  prcunqu  7257  genpdisj  7295  cauappcvgprlemrnd  7422  caucvgprlemrnd  7445  caucvgprprlemrnd  7473  nn0n0n1ge2b  9081  fzind  9117  icoshft  9713  fzen  9763  seq3coll  10525  shftuz  10529  mulgcd  11600  algcvga  11628  lcmneg  11651  blssps  12491  blss  12492  metcnp3  12575
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