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Axiom ax-5 1544
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 4 . . 3  wff  ( ph  ->  ps )
4 vx . . 3  set  x
53, 4wal 1527 . 2  wff  A. x
( ph  ->  ps )
61, 4wal 1527 . . 3  wff  A. x ph
72, 4wal 1527 . . 3  wff  A. x ps
86, 7wi 4 . 2  wff  ( A. x ph  ->  A. x ps )
95, 8wi 4 1  wff  ( A. x ( ph  ->  ps )  ->  ( A. x ph  ->  A. x ps ) )
Colors of variables: wff set class
This axiom is referenced by:  alim  1545  alimi  1546  spfw  1657  spw  1660  ax5o  1717  a16g  1885  stoweidlem61  27810  3ax5  28300  3ax5VD  28638  hbalgVD  28681
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