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Theorem dveeq2-o 2262
 Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq2 2078 using ax-11o 2219. (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dveeq2-o
Distinct variable group:   ,

Proof of Theorem dveeq2-o
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-17 1627 . 2
2 ax-17 1627 . 2
3 equequ2 1699 . 2
41, 2, 3dvelimf-o 2258 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1550 This theorem is referenced by:  ax11eq  2271  ax11el  2272  ax11inda  2278  ax11v2-o  2279 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-4 2213  ax-5o 2214  ax-6o 2215  ax-10o 2217  ax-12o 2220 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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