Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  aecoms-o Structured version   Visualization version   GIF version

Theorem aecoms-o 35050
Description: A commutation rule for identical variable specifiers. Version of aecoms 2393 using ax-c11 35035. (Contributed by NM, 10-May-1993.) (Proof modification is discouraged.) (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 35049 . 2 (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
2 alequcoms-o.1 . 2 (∀𝑥 𝑥 = 𝑦𝜑)
31, 2syl 17 1 (∀𝑦 𝑦 = 𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1599
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-c5 35031  ax-c4 35032  ax-c7 35033  ax-c10 35034  ax-c11 35035  ax-c9 35038
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824
This theorem is referenced by:  hbae-o  35051  dral1-o  35052  dvelimf-o  35077  aev-o  35079  ax12indalem  35093  ax12inda2ALT  35094
  Copyright terms: Public domain W3C validator