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Theorem sbelx 2124
Description: Elimination of substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbelx (φx(x = y [x / y]φ))
Distinct variable groups:   x,y   φ,x
Allowed substitution hint:   φ(y)

Proof of Theorem sbelx
StepHypRef Expression
1 sbid2v 2123 . 2 ([y / x][x / y]φφ)
2 sb5 2100 . 2 ([y / x][x / y]φx(x = y [x / y]φ))
31, 2bitr3i 242 1 (φx(x = y [x / y]φ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358  wex 1541  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  sbel2x  2125
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