Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-cbv3hv2 Structured version   Visualization version   Unicode version

Theorem bj-cbv3hv2 31395
Description: Version of cbv3h 2122 with two dv conditions, which does not require ax-11 1937 nor ax-13 2104. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-cbv3hv2.nf  |-  ( ps 
->  A. x ps )
bj-cbv3hv2.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
bj-cbv3hv2  |-  ( A. x ph  ->  A. y ps )
Distinct variable groups:    x, y    ph, y
Allowed substitution hints:    ph( x)    ps( x, y)

Proof of Theorem bj-cbv3hv2
StepHypRef Expression
1 bj-cbv3hv2.nf . . 3  |-  ( ps 
->  A. x ps )
21nfi 1682 . 2  |-  F/ x ps
3 bj-cbv3hv2.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
42, 3bj-cbv3v2 31394 1  |-  ( A. x ph  ->  A. y ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator