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Theorem sbid2h 1726
Description: An identity law for substitution. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
sbid2h.1 (φxφ)
Assertion
Ref Expression
sbid2h ([y / x][x / y]φφ)

Proof of Theorem sbid2h
StepHypRef Expression
1 sbid2h.1 . . 3 (φxφ)
21sbcof2 1688 . 2 ([y / x][x / y]φ ↔ [y / x]φ)
31sbh 1656 . 2 ([y / x]φφ)
42, 3bitri 173 1 ([y / x][x / y]φφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1240  [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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbid2  1727  sb5rf  1729  sb6rf  1730  sbid2v  1869
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