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Theorem sb6 1705
Description: Equivalence for substitution. Compare Theorem 6.2 of [Quine] p. 40. Also proved as Lemmas 16 and 17 of [Tarski] p. 70.
Assertion
Ref Expression
sb6
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb6
StepHypRef Expression
1 sb56 1704 . . 3
21anbi2i 431 . 2
3 df-sb 1606 . 2
4 ax-4 1392 . . 3
54pm4.71ri 371 . 2
62, 3, 53bitr4i 200 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 96   wb 97  wal 1335  wex 1374
This theorem is referenced by:  sb5  1706  2sb6  1781  sb6a  1784  exsb  1797  sbal2  1805
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100  ax-in1 527  ax-in2 528  ax-io 607  ax-5 1336  ax-6 1337  ax-7 1338  ax-gen 1339  ax-ie1 1375  ax-ie2 1376  ax-8 1387  ax-10 1388  ax-11 1389  ax-i12 1391  ax-4 1392  ax-17 1402  ax-i9 1417  ax-ial 1430  ax-i5r 1431  ax-16 1644
This theorem depends on definitions:  df-bi 109  df-sb 1606
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