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Theorem dveeq1-o 2263
 Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq1 2021 using ax-10o . (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dveeq1-o
Distinct variable group:   ,

Proof of Theorem dveeq1-o
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-17 1626 . 2
2 ax-17 1626 . 2
3 equequ1 1696 . 2
41, 2, 3dvelimf-o 2256 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem is referenced by:  ax11inda2ALT  2274 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-4 2211  ax-5o 2212  ax-6o 2213  ax-10o 2215  ax-12o 2218 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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