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Theorem equsb3 2102
 Description: Substitution applied to an atomic wff. (Contributed by Raph Levien and FL, 4-Dec-2005.)
Assertion
Ref Expression
equsb3 ([x / y]y = zx = z)
Distinct variable group:   y,z

Proof of Theorem equsb3
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 equsb3lem 2101 . . 3 ([w / y]y = zw = z)
21sbbii 1653 . 2 ([x / w][w / y]y = z ↔ [x / w]w = z)
3 nfv 1619 . . 3 w y = z
43sbco2 2086 . 2 ([x / w][w / y]y = z ↔ [x / y]y = z)
5 equsb3lem 2101 . 2 ([x / w]w = zx = z)
62, 4, 53bitr3i 266 1 ([x / y]y = zx = z)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  [wsb 1648 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by:  sb8eu  2222  sb8iota  4346
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