NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  dveeq1-o Unicode version

Theorem dveeq1-o 2187
Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq1 2018 using ax-10o . (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dveeq1-o
Distinct variable group:   ,

Proof of Theorem dveeq1-o
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-17 1616 . 2
2 ax-17 1616 . 2
3 equequ1 1684 . 2
41, 2, 3dvelimf-o 2180 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-4 2135  ax-5o 2136  ax-6o 2137  ax-10o 2139  ax-12o 2142
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  ax11inda2ALT  2198
  Copyright terms: Public domain W3C validator