MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dral2 Unicode version

Theorem dral2 2051
Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.) (Revised by Wolf Lammen, 4-Mar-2018.)
Hypothesis
Ref Expression
dral1.1  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
Assertion
Ref Expression
dral2  |-  ( A. x  x  =  y  ->  ( A. z ph  <->  A. z ps ) )

Proof of Theorem dral2
StepHypRef Expression
1 nfae 2042 . 2  |-  F/ z A. x  x  =  y
2 dral1.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2albid 1788 1  |-  ( A. x  x  =  y  ->  ( A. z ph  <->  A. z ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549
This theorem is referenced by:  dral1  2053  drnf2OLD  2059  equveliOLD  2082  sbal1  2202  drnfc1  2587  drnfc2  2588  axpownd  8465
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
  Copyright terms: Public domain W3C validator