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Axiom ax-i5r 1444
Description: Axiom of quantifier collection. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-i5r  |-  ( ( A. x ph  ->  A. x ps )  ->  A. x ( A. x ph  ->  ps ) )

Detailed syntax breakdown of Axiom ax-i5r
StepHypRef Expression
1 wph . . . 4  wff  ph
2 vx . . . 4  setvar  x
31, 2wal 1257 . . 3  wff  A. x ph
4 wps . . . 4  wff  ps
54, 2wal 1257 . . 3  wff  A. x ps
63, 5wi 4 . 2  wff  ( A. x ph  ->  A. x ps )
73, 4wi 4 . . 3  wff  ( A. x ph  ->  ps )
87, 2wal 1257 . 2  wff  A. x
( A. x ph  ->  ps )
96, 8wi 4 1  wff  ( ( A. x ph  ->  A. x ps )  ->  A. x ( A. x ph  ->  ps ) )
Colors of variables: wff set class
This axiom is referenced by:  hbim  1453  hbimd  1481
  Copyright terms: Public domain W3C validator