ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  reximi2 Unicode version

Theorem reximi2 2566
Description: Inference quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 8-Nov-2004.)
Hypothesis
Ref Expression
reximi2.1  |-  ( ( x  e.  A  /\  ph )  ->  ( x  e.  B  /\  ps )
)
Assertion
Ref Expression
reximi2  |-  ( E. x  e.  A  ph  ->  E. x  e.  B  ps )

Proof of Theorem reximi2
StepHypRef Expression
1 reximi2.1 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ( x  e.  B  /\  ps )
)
21eximi 1593 . 2  |-  ( E. x ( x  e.  A  /\  ph )  ->  E. x ( x  e.  B  /\  ps ) )
3 df-rex 2454 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
4 df-rex 2454 . 2  |-  ( E. x  e.  B  ps  <->  E. x ( x  e.  B  /\  ps )
)
52, 3, 43imtr4i 200 1  |-  ( E. x  e.  A  ph  ->  E. x  e.  B  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   E.wex 1485    e. wcel 2141   E.wrex 2449
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-rex 2454
This theorem is referenced by:  btwnz  9331  ioo0  10216
  Copyright terms: Public domain W3C validator