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Theorem aecoms 2427
Description: A commutation rule for identical variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 2371. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
aecoms.1 (∀𝑥 𝑥 = 𝑦𝜑)
Assertion
Ref Expression
aecoms (∀𝑦 𝑦 = 𝑥𝜑)

Proof of Theorem aecoms
StepHypRef Expression
1 aecom 2426 . 2 (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2 aecoms.1 . 2 (∀𝑥 𝑥 = 𝑦𝜑)
31, 2sylbi 216 1 (∀𝑦 𝑦 = 𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1539
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-12 2171  ax-13 2371
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782  df-nf 1786
This theorem is referenced by:  axc11  2429  nd4  10584  axrepnd  10588  axpownd  10595  axregnd  10598  axinfnd  10600  axacndlem5  10605  axacnd  10606  wl-ax11-lem1  36442  wl-ax11-lem3  36444  wl-ax11-lem9  36450  wl-ax11-lem10  36451  e2ebind  43314
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