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Theorem equsb3rOLD 2104
 Description: Obsolete version of equsb3r 2103 as of 2-Sep-2023. (Contributed by AV, 29-Jul-2023.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equsb3rOLD ([𝑦 / 𝑥]𝑧 = 𝑥𝑧 = 𝑦)
Distinct variable group:   𝑥,𝑧

Proof of Theorem equsb3rOLD
StepHypRef Expression
1 equcom 2018 . . 3 (𝑧 = 𝑥𝑥 = 𝑧)
21sbbii 2074 . 2 ([𝑦 / 𝑥]𝑧 = 𝑥 ↔ [𝑦 / 𝑥]𝑥 = 𝑧)
3 equsb3 2102 . 2 ([𝑦 / 𝑥]𝑥 = 𝑧𝑦 = 𝑧)
4 equcom 2018 . 2 (𝑦 = 𝑧𝑧 = 𝑦)
52, 3, 43bitri 298 1 ([𝑦 / 𝑥]𝑧 = 𝑥𝑧 = 𝑦)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 207  [wsb 2062 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008 This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1774  df-sb 2063 This theorem is referenced by: (None)
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