ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbequ Structured version   Unicode version

Theorem sbequ 1718
Description: An equality theorem for substitution. Used in proof of Theorem 9.7 in [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequ

Proof of Theorem sbequ
StepHypRef Expression
1 sbequi 1717 . 2
2 sbequi 1717 . . 3
32equcoms 1591 . 2
41, 3impbid 120 1
Colors of variables: wff set class
Syntax hints:   wi 4   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:  drsb2  1719  sbco2vlem  1817  sbco2yz  1834  sbcocom  1841  sb10f  1868  hbsb4  1885  nfsb4or  1896  sb8eu  1910  sb8euh  1920  cbvab  2157  cbvralf  2521  cbvrexf  2522  cbvreu  2525  cbvralsv  2538  cbvrexsv  2539  cbvrab  2549  cbvreucsf  2904  cbvrabcsf  2905  sbss  3323  cbvopab1  3821  cbvmpt  3842  tfis  4249  findes  4269  cbviota  4815  sb8iota  4817  cbvriota  5421  uzind4s  8289  cbvrald  9242  setindft  9395
  Copyright terms: Public domain W3C validator