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Theorem barbariALT 2702
Description: Alternate proof of barbari 2701, shorter but using more axioms. See comment of dariiALT 2698. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
barbari.maj 𝑥(𝜑𝜓)
barbari.min 𝑥(𝜒𝜑)
barbari.e 𝑥𝜒
Assertion
Ref Expression
barbariALT 𝑥(𝜒𝜓)

Proof of Theorem barbariALT
StepHypRef Expression
1 barbari.e . 2 𝑥𝜒
2 barbari.maj . . . . 5 𝑥(𝜑𝜓)
3 barbari.min . . . . 5 𝑥(𝜒𝜑)
42, 3barbara 2695 . . . 4 𝑥(𝜒𝜓)
54spi 2168 . . 3 (𝜒𝜓)
65ancli 544 . 2 (𝜒 → (𝜒𝜓))
71, 6eximii 1880 1 𝑥(𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386  wal 1599  wex 1823
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-12 2163
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824
This theorem is referenced by: (None)
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