ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax9o Structured version   Unicode version

Theorem ax9o 1585
Description: An implication related to substitution. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.)
Assertion
Ref Expression
ax9o

Proof of Theorem ax9o
StepHypRef Expression
1 a9e 1583 . 2
2 19.29r 1509 . . 3
3 hba1 1430 . . . . 5
4 pm3.35 329 . . . . 5
53, 4exlimih 1481 . . . 4
6 ax-4 1397 . . . 4
75, 6syl 14 . . 3
82, 7syl 14 . 2
91, 8mpan 400 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240   wceq 1242  wex 1378
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-4 1397  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  equsalh  1611  spimth  1620  spimh  1622
  Copyright terms: Public domain W3C validator