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Theorem sb1 1724
Description: One direction of a simplified definition of substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sb1 ([𝑦 / 𝑥]𝜑 → ∃𝑥(𝑥 = 𝑦𝜑))

Proof of Theorem sb1
StepHypRef Expression
1 df-sb 1721 . 2 ([𝑦 / 𝑥]𝜑 ↔ ((𝑥 = 𝑦𝜑) ∧ ∃𝑥(𝑥 = 𝑦𝜑)))
21simprbi 273 1 ([𝑦 / 𝑥]𝜑 → ∃𝑥(𝑥 = 𝑦𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wex 1453  [wsb 1720
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116  df-sb 1721
This theorem is referenced by:  sbh  1734  sbiedh  1745  sb4a  1757  sb4e  1761  sbcof2  1766  sb4  1788  sb4or  1789  spsbe  1798  sbidm  1807  sb5rf  1808  bj-sbimedh  12905
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