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Theorem equcomi1 35916
Description: Proof of equcomi 2015 from equid1 35915, avoiding use of ax-5 1902 (the only use of ax-5 1902 is via ax7 2014, so using ax-7 2006 instead would remove dependency on ax-5 1902). (Contributed by BJ, 8-Jul-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equcomi1 (𝑥 = 𝑦𝑦 = 𝑥)

Proof of Theorem equcomi1
StepHypRef Expression
1 equid1 35915 . 2 𝑥 = 𝑥
2 ax7 2014 . 2 (𝑥 = 𝑦 → (𝑥 = 𝑥𝑦 = 𝑥))
31, 2mpi 20 1 (𝑥 = 𝑦𝑦 = 𝑥)
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-c5 35899  ax-c4 35900  ax-c7 35901  ax-c10 35902  ax-c9 35906
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772
This theorem is referenced by:  aecom-o  35917
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