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Axiom ax-5 1545
Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ax-5  |-  ( A. x ( ph  ->  ps )  ->  ( A. x ph  ->  A. x ps ) )

Detailed syntax breakdown of Axiom ax-5
StepHypRef Expression
1 wph . . . 4  wff  ph
2 wps . . . 4  wff  ps
31, 2wi 6 . . 3  wff  ( ph  ->  ps )
4 vx . . 3  set  x
53, 4wal 1528 . 2  wff  A. x
( ph  ->  ps )
61, 4wal 1528 . . 3  wff  A. x ph
72, 4wal 1528 . . 3  wff  A. x ps
86, 7wi 6 . 2  wff  ( A. x ph  ->  A. x ps )
95, 8wi 6 1  wff  ( A. x ( ph  ->  ps )  ->  ( A. x ph  ->  A. x ps ) )
Colors of variables: wff set class
This axiom is referenced by:  alim  1546  alimi  1547  spfw  1658  spw  1661  ax5o  1719  a16gALT  1887  stoweidlem61  27210  3ax5  27572  3ax5VD  27907  hbalgVD  27950
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