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Theorem 2a1dd 51
Description: Double deduction introducing two antecedents. Two applications of 2a1dd 51. Deduction associated with 2a1d 26. Double deduction associated with 2a1 28 and 2a1i 12. (Contributed by Jeff Hankins, 5-Aug-2009.)
Hypothesis
Ref Expression
2a1dd.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
2a1dd (𝜑 → (𝜓 → (𝜃 → (𝜏𝜒))))

Proof of Theorem 2a1dd
StepHypRef Expression
1 2a1dd.1 . . 3 (𝜑 → (𝜓𝜒))
21a1dd 50 . 2 (𝜑 → (𝜓 → (𝜏𝜒)))
32a1dd 50 1 (𝜑 → (𝜓 → (𝜃 → (𝜏𝜒))))
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  1216  ad5ant14OLD  1218  ad5ant15OLD  1220  ad5ant23OLD  1222  ad5ant24OLD  1224  ad5ant25OLD  1226  ad5ant125OLD  1465
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