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Axiom ax-ial 1527
Description:  x is not free in  A. x ph. One of the axioms of predicate logic. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-ial  |-  ( A. x ph  ->  A. x A. x ph )

Detailed syntax breakdown of Axiom ax-ial
StepHypRef Expression
1 wph . . 3  wff  ph
2 vx . . 3  setvar  x
31, 2wal 1346 . 2  wff  A. x ph
43, 2wal 1346 . 2  wff  A. x A. x ph
53, 4wi 4 1  wff  ( A. x ph  ->  A. x A. x ph )
Colors of variables: wff set class
This axiom is referenced by:  hba1  1533  ax6b  1644  exdistrfor  1793  sbcof2  1803  hbs1  1931  sbcomxyyz  1965
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