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Theorem sb4bor 1732
 Description: Simplified definition of substitution when variables are distinct, expressed via disjunction. (Contributed by Jim Kingdon, 18-Mar-2018.)
Assertion
Ref Expression
sb4bor

Proof of Theorem sb4bor
StepHypRef Expression
1 sb4or 1730 . 2
2 sb2 1666 . . . . 5
3 df-bi 114 . . . . . 6
43simpri 110 . . . . 5
52, 4mpan2 409 . . . 4
65alimi 1360 . . 3
76orim2i 688 . 2
81, 7ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   wo 639  wal 1257  wsb 1661 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662 This theorem is referenced by: (None)
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