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Theorem exp4a 364
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp4a.1 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
Assertion
Ref Expression
exp4a (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp4a
StepHypRef Expression
1 exp4a.1 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
2 impexp 261 . 2 (((𝜒𝜃) → 𝜏) ↔ (𝜒 → (𝜃𝜏)))
31, 2syl6ib 160 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:  exp4b  365  exp4d  367  exp45  372  exp5c  374  tfri3  6272  nnmordi  6420  fiintim  6825  ndvdssub  11663  iscnp4  12426  metcnp3  12719
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