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Theorem equsb3 1822
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 1821 . . 3 ([w / y]y = zw = z)
21sbbii 1645 . 2 ([x / w][w / y]y = z ↔ [x / w]w = z)
3 ax-17 1416 . . 3 (y = zw y = z)
43sbco2v 1818 . 2 ([x / w][w / y]y = z ↔ [x / y]y = z)
5 equsb3lem 1821 . 2 ([x / w]w = zx = z)
62, 4, 53bitr3i 199 1 ([x / y]y = zx = z)
Colors of variables: wff set class
Syntax hints:  wb 98  [wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  sb8eu  1910  sb8euh  1920  sb8iota  4817
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