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Theorem equcomi1 33203
Description: Proof of equcomi 1931 from equid1 33202, avoiding use of ax-5 1827 (the only use of ax-5 1827 is via ax7 1930, so using ax-7 1922 instead would remove dependency on ax-5 1827). (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 33202 . 2 𝑥 = 𝑥
2 ax7 1930 . 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 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-c5 33186  ax-c4 33187  ax-c7 33188  ax-c10 33189  ax-c9 33193
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696
This theorem is referenced by:  aecom-o  33204
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