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Theorem exp4d 636
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp4d.1 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
Assertion
Ref Expression
exp4d (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp4d
StepHypRef Expression
1 exp4d.1 . . 3 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
21expd 452 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32exp4a 632 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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-an 386
This theorem is referenced by:  tfrlem9  7426  omass  7605  pssnn  8122  cardinfima  8864  ltexprlem7  9808  facdiv  13014  infpnlem1  15538  atcvatlem  29090  mdsymlem5  29112  mdsymlem7  29114  btwnconn1lem11  31843  exp5k  31937
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