MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  daraptiALT Structured version   Visualization version   GIF version

Theorem daraptiALT 2750
Description: Alternate proof of darapti 2749, shorter but using more axioms. See comment of dariiALT 2731. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
darapti.maj 𝑥(𝜑𝜓)
darapti.min 𝑥(𝜑𝜒)
darapti.e 𝑥𝜑
Assertion
Ref Expression
daraptiALT 𝑥(𝜒𝜓)

Proof of Theorem daraptiALT
StepHypRef Expression
1 darapti.e . 2 𝑥𝜑
2 darapti.min . . . 4 𝑥(𝜑𝜒)
32spi 2182 . . 3 (𝜑𝜒)
4 darapti.maj . . . 4 𝑥(𝜑𝜓)
54spi 2182 . . 3 (𝜑𝜓)
63, 5jca 515 . 2 (𝜑 → (𝜒𝜓))
71, 6eximii 1838 1 𝑥(𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wal 1536  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2176
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator