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Theorem a1ddd 80
Description: Triple deduction introducing an antecedent to a wff. Deduction associated with a1dd 50. Double deduction associated with a1d 25. Triple deduction associated with ax-1 6 and a1i 11. (Contributed by Jeff Hankins, 4-Aug-2009.)
Hypothesis
Ref Expression
a1ddd.1 (𝜑 → (𝜓 → (𝜒𝜏)))
Assertion
Ref Expression
a1ddd (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem a1ddd
StepHypRef Expression
1 a1ddd.1 . 2 (𝜑 → (𝜓 → (𝜒𝜏)))
2 ax-1 6 . 2 (𝜏 → (𝜃𝜏))
31, 2syl8 76 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  ad5ant13OLD  759  ad5ant14OLD  761  ad5ant15OLD  763  ad5ant23OLD  765  ad5ant24OLD  767  ad5ant25OLD  769  ad4ant123OLD  1207  ad5ant234OLD  1466  ad5ant235OLD  1468  ad5ant123OLD  1470  ad5ant124OLD  1472  ad5ant134OLD  1476  ad5ant135OLD  1478
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