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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:  ad4ant123  1291  ad5ant13  1298  ad5ant14  1299  ad5ant15  1300  ad5ant23  1301  ad5ant24  1302  ad5ant25  1303  ad5ant234  1305  ad5ant235  1306  ad5ant123  1307  ad5ant124  1308  ad5ant134  1310  ad5ant135  1311
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