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Axiom ax-4 1602
Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105 and Theorem 19.20 of [Margaris] p. 90. It is restated as alim 1603 for labelling consistency. It should be used only by alim 1603. (Contributed by NM, 21-May-2008.) (New usage is discouraged.)
Assertion
Ref Expression
ax-4  |-  ( A. x ( ph  ->  ps )  ->  ( A. x ph  ->  A. x ps ) )

Detailed syntax breakdown of Axiom ax-4
StepHypRef Expression
1 wph . . . 4  wff  ph
2 wps . . . 4  wff  ps
31, 2wi 4 . . 3  wff  ( ph  ->  ps )
4 vx . . 3  setvar  x
53, 4wal 1367 . 2  wff  A. x
( ph  ->  ps )
61, 4wal 1367 . . 3  wff  A. x ph
72, 4wal 1367 . . 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 setvar class
This axiom is referenced by:  alim  1603
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