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Theorem equcomi 1661
Description: Commutative law for equality. Lemma 7 of [Tarski] p. 69. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equcomi (𝑥 = 𝑦𝑦 = 𝑥)

Proof of Theorem equcomi
StepHypRef Expression
1 equid 1658 . 2 𝑥 = 𝑥
2 ax-8 1463 . 2 (𝑥 = 𝑦 → (𝑥 = 𝑥𝑦 = 𝑥))
31, 2mpi 15 1 (𝑥 = 𝑦𝑦 = 𝑥)
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-gen 1406  ax-ie2 1451  ax-8 1463  ax-17 1487  ax-i9 1491
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ax6evr  1662  equcom  1663  equcoms  1665  ax10  1676  cbv2h  1705  equvini  1712  equveli  1713  equsb2  1740  drex1  1750  sbcof2  1762  aev  1764  cbvexdh  1874  rext  4095  iotaval  5055
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