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Theorem aecoms 2431
Description: A commutation rule for identical variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 2375. (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 2430 . 2 (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2 aecoms.1 . 2 (∀𝑥 𝑥 = 𝑦𝜑)
31, 2sylbi 217 1 (∀𝑦 𝑦 = 𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1535
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-12 2175  ax-13 2375
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-nf 1781
This theorem is referenced by:  axc11  2433  nd4  10628  axrepnd  10632  axpownd  10639  axregnd  10642  axinfnd  10644  axacndlem5  10649  axacnd  10650  wl-ax11-lem1  37566  wl-ax11-lem3  37568  wl-ax11-lem9  37574  wl-ax11-lem10  37575  e2ebind  44561
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