MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  axc4i Structured version   Unicode version

Theorem axc4i 1955
Description: Inference version of axc4 1913. (Contributed by NM, 3-Jan-1993.)
Hypothesis
Ref Expression
axc4i.1  |-  ( A. x ph  ->  ps )
Assertion
Ref Expression
axc4i  |-  ( A. x ph  ->  A. x ps )

Proof of Theorem axc4i
StepHypRef Expression
1 nfa1 1954 . 2  |-  F/ x A. x ph
2 axc4i.1 . 2  |-  ( A. x ph  ->  ps )
31, 2alrimi 1930 1  |-  ( A. x ph  ->  A. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664
This theorem is referenced by:  hbae  2111  hbsb2  2153  hbsb2a  2155  hbsb2e  2156  reu6  3266  axunndlem1  9018  axregndOLD  9028  axacndlem3  9033  axacndlem5  9035  axacnd  9036  bj-nfs1t  31054  bj-hbsb2v  31119  bj-hbsb2av  31121  bj-hbaeb2  31171  frege93  36189  pm11.57  36376  pm11.59  36378  axc5c4c711toc7  36392  axc11next  36394  hbalg  36559  ax6e2eq  36561  ax6e2eqVD  36944
  Copyright terms: Public domain W3C validator