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Theorem aecoms-o 36916
Description: A commutation rule for identical variable specifiers. Version of aecoms 2428 using ax-c11 36901. (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 36915 . 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 1537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-c5 36897  ax-c4 36898  ax-c7 36899  ax-c10 36900  ax-c11 36901  ax-c9 36904
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783
This theorem is referenced by:  hbae-o  36917  dral1-o  36918  dvelimf-o  36943  aev-o  36945  ax12indalem  36959  ax12inda2ALT  36960
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