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Theorem dveeq2-o 2263
Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq2 2042 using ax-c15 2220. (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-5 1704 . 2
2 ax-5 1704 . 2
3 equequ2 1799 . 2
41, 2, 3dvelimf-o 2259 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393
This theorem is referenced by:  ax12eq  2271  ax12el  2272  ax12inda  2278  ax12v2-o  2279
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c9 2221
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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