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Theorem equcomi 2102
Description: Commutative law for equality. Equality is a symmetric relation. Lemma 3 of [KalishMontague] p. 85. See also Lemma 7 of [Tarski] p. 69. (Contributed by NM, 10-Jan-1993.) (Revised by NM, 9-Apr-2017.)
Assertion
Ref Expression
equcomi (𝑥 = 𝑦𝑦 = 𝑥)

Proof of Theorem equcomi
StepHypRef Expression
1 equid 2097 . 2 𝑥 = 𝑥
2 ax7 2101 . 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 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853
This theorem is referenced by:  equcom  2103  equcoms  2105  ax13dgen2  2170  cbv2h  2430  axc16i  2472  equsb2  2516  axsep  4915  rext  5045  soxp  7442  axextnd  9616  prodmo  14874  mpt2matmul  20471  finminlem  32650  bj-ssbid2ALT  32984  axc11n11  33010  axc11n11r  33011  bj-cbv2hv  33068  bj-axsep  33130  ax6er  33156  poimirlem25  33768  axc11nfromc11  34735  aev-o  34740
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