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Theorem equcomi 1635
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 1632 . 2 𝑥 = 𝑥
2 ax-8 1438 . 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 104  ax-gen 1381  ax-ie2 1426  ax-8 1438  ax-17 1462  ax-i9 1466
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ax6evr  1636  equcom  1637  equcoms  1638  ax10  1649  cbv2h  1678  equvini  1685  equveli  1686  equsb2  1713  drex1  1723  sbcof2  1735  aev  1737  cbvexdh  1846  rext  4016  iotaval  4957
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