ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  r19.29a Unicode version

Theorem r19.29a 2499
Description: A commonly used pattern based on r19.29 2495 (Contributed by Thierry Arnoux, 22-Nov-2017.)
Hypotheses
Ref Expression
r19.29a.1  |-  ( ( ( ph  /\  x  e.  A )  /\  ps )  ->  ch )
r19.29a.2  |-  ( ph  ->  E. x  e.  A  ps )
Assertion
Ref Expression
r19.29a  |-  ( ph  ->  ch )
Distinct variable groups:    ch, x    ph, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem r19.29a
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
2 r19.29a.1 . 2  |-  ( ( ( ph  /\  x  e.  A )  /\  ps )  ->  ch )
3 r19.29a.2 . 2  |-  ( ph  ->  E. x  e.  A  ps )
41, 2, 3r19.29af 2498 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    e. wcel 1434   E.wrex 2350
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-ral 2354  df-rex 2355
This theorem is referenced by:  cnegexlem3  7352  cnegex  7353  modqmuladdnn0  9450
  Copyright terms: Public domain W3C validator