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Theorem abcdta 43959
Description: Given (((a and b) and c) and d), there exists a proof for a. (Contributed by Jarvin Udandy, 3-Sep-2016.)
Hypothesis
Ref Expression
abcdta.1 (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃)
Assertion
Ref Expression
abcdta 𝜑

Proof of Theorem abcdta
StepHypRef Expression
1 abcdta.1 . . . 4 (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃)
21simpli 487 . . 3 ((𝜑𝜓) ∧ 𝜒)
32simpli 487 . 2 (𝜑𝜓)
43simpli 487 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 399
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210  df-an 400
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator