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Theorem sb4or 1711
Description: One direction of a simplified definition of substitution when variables are distinct. Similar to sb4 1710 but stronger in intuitionistic logic. (Contributed by Jim Kingdon, 2-Feb-2018.)
Assertion
Ref Expression
sb4or

Proof of Theorem sb4or
StepHypRef Expression
1 equs5or 1708 . 2
2 nfe1 1382 . . . . . 6  F/
3 nfa1 1431 . . . . . 6  F/
42, 3nfim 1461 . . . . 5  F/
54nfri 1409 . . . 4
6 sb1 1646 . . . . 5
76imim1i 54 . . . 4
85, 7alrimih 1355 . . 3
98orim2i 677 . 2
101, 9ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wo 628  wal 1240  wex 1378  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:  sb4bor  1713  nfsb2or  1715
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