MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  reximddv Structured version   Unicode version

Theorem reximddv 2850
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Thierry Arnoux, 7-Dec-2016.)
Hypotheses
Ref Expression
reximddva.1  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
reximddva.2  |-  ( ph  ->  E. x  e.  A  ps )
Assertion
Ref Expression
reximddv  |-  ( ph  ->  E. x  e.  A  ch )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem reximddv
StepHypRef Expression
1 reximddva.2 . 2  |-  ( ph  ->  E. x  e.  A  ps )
2 reximddva.1 . . . 4  |-  ( (
ph  /\  ( x  e.  A  /\  ps )
)  ->  ch )
32expr 615 . . 3  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
43reximdva 2849 . 2  |-  ( ph  ->  ( E. x  e.  A  ps  ->  E. x  e.  A  ch )
)
51, 4mpd 15 1  |-  ( ph  ->  E. x  e.  A  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    e. wcel 1756   E.wrex 2737
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1587  df-nf 1590  df-ral 2741  df-rex 2742
This theorem is referenced by:  xrge0tsms  20433  legov  23038  legtrid  23044  midexlem  23108  xrge0tsmsd  26275  ballotlemfc0  26897  ballotlemfcc  26898  stoweidlem27  29848  scmatsubcl  30923  scmatmulcl  30925
  Copyright terms: Public domain W3C validator