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Theorem aecoms 2442
Description: A commutation rule for identical variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 2382. (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 2441 . 2 (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦)
2 aecoms.1 . 2 (∀𝑥 𝑥 = 𝑦𝜑)
31, 2sylbi 220 1 (∀𝑦 𝑦 = 𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536
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 1911  ax-6 1970  ax-7 2015  ax-10 2143  ax-12 2176  ax-13 2382
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786
This theorem is referenced by:  axc11  2444  nd4  10005  axrepnd  10009  axpownd  10016  axregnd  10019  axinfnd  10021  axacndlem5  10026  axacnd  10027  wl-ax11-lem1  34981  wl-ax11-lem3  34983  wl-ax11-lem9  34989  wl-ax11-lem10  34990  e2ebind  41262
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