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Theorem aecoms 2419
Description: A commutation rule for identical variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 2363. (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 2418 . 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 1531
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-12 2163  ax-13 2363
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-nf 1778
This theorem is referenced by:  axc11  2421  nd4  10581  axrepnd  10585  axpownd  10592  axregnd  10595  axinfnd  10597  axacndlem5  10602  axacnd  10603  wl-ax11-lem1  36937  wl-ax11-lem3  36939  wl-ax11-lem9  36945  wl-ax11-lem10  36946  e2ebind  43813
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