MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  a5i-o Unicode version

Theorem a5i-o 2089
Description: Inference version of ax-5o 2075. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
a5i-o.1  |-  ( A. x ph  ->  ps )
Assertion
Ref Expression
a5i-o  |-  ( A. x ph  ->  A. x ps )

Proof of Theorem a5i-o
StepHypRef Expression
1 hba1-o 2088 . 2  |-  ( A. x ph  ->  A. x A. x ph )
2 a5i-o.1 . 2  |-  ( A. x ph  ->  ps )
31, 2alrimih 1552 1  |-  ( A. x ph  ->  A. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  hbae-o  2092  aev-o  2121  ax10-16  2129  ax11indalem  2136  ax11inda2ALT  2137
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-4 2074  ax-5o 2075  ax-6o 2076
  Copyright terms: Public domain W3C validator