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Theorem mosub 2742
 Description: "At most one" remains true after substitution. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
mosub.1 ∃*𝑥𝜑
Assertion
Ref Expression
mosub ∃*𝑥𝑦(𝑦 = 𝐴𝜑)
Distinct variable group:   𝑥,𝑦,𝐴
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem mosub
StepHypRef Expression
1 mosubt 2741 . 2 (∀𝑦∃*𝑥𝜑 → ∃*𝑥𝑦(𝑦 = 𝐴𝜑))
2 mosub.1 . 2 ∃*𝑥𝜑
31, 2mpg 1356 1 ∃*𝑥𝑦(𝑦 = 𝐴𝜑)
 Colors of variables: wff set class Syntax hints:   ∧ wa 101   = wceq 1259  ∃wex 1397  ∃*wmo 1917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576 This theorem is referenced by: (None)
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