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 36559
Description: A commutation rule for identical variable specifiers. Version of aecoms 2428 using ax-c11 36544. (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 36558 . 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 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-c5 36540  ax-c4 36541  ax-c7 36542  ax-c10 36543  ax-c11 36544  ax-c9 36547
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787
This theorem is referenced by:  hbae-o  36560  dral1-o  36561  dvelimf-o  36586  aev-o  36588  ax12indalem  36602  ax12inda2ALT  36603
  Copyright terms: Public domain W3C validator