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Theorem exp43 369
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp43.1 (((𝜑𝜓) ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
exp43 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp43
StepHypRef Expression
1 exp43.1 . . 3 (((𝜑𝜓) ∧ (𝜒𝜃)) → 𝜏)
21ex 114 . 2 ((𝜑𝜓) → ((𝜒𝜃) → 𝜏))
32exp4b 364 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
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
This theorem is referenced by:  exp53  374  funssres  5160  fvopab3ig  5488  fvmptt  5505  tfri3  6257  nnmordi  6405  fiintim  6810  ordiso2  6913  qaddcl  9420  qmulcl  9422  bernneq  10405  opnneissb  12313  txbas  12416
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