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

Theorem aecoms-o 2152
 Description: A commutation rule for identical variable specifiers. Version of aecoms 1947 using ax-10o . (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
alequcoms-o.1 (x x = yφ)
Assertion
Ref Expression
aecoms-o (y y = xφ)

Proof of Theorem aecoms-o
StepHypRef Expression
1 aecom-o 2151 . 2 (y y = xx x = y)
2 alequcoms-o.1 . 2 (x x = yφ)
31, 2syl 15 1 (y y = xφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-10o 2139 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by:  hbae-o  2153  dral1-o  2154  dvelimf-o  2180  aev-o  2182  ax11indalem  2197  ax11inda2ALT  2198
 Copyright terms: Public domain W3C validator