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Theorem aecoms-o 34506
Description: A commutation rule for identical variable specifiers. Version of aecoms 2345 using ax-c11 34491. (Contributed by NM, 10-May-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 34505 . 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 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-c5 34487  ax-c4 34488  ax-c7 34489  ax-c10 34490  ax-c11 34491  ax-c9 34494
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745
This theorem is referenced by:  hbae-o  34507  dral1-o  34508  dvelimf-o  34533  aev-o  34535  ax12indalem  34549  ax12inda2ALT  34550
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