Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  strlem2 Structured version   Unicode version

Theorem strlem2 23746
 Description: Lemma for strong state theorem. (Contributed by NM, 28-Oct-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
strlem2.1
Assertion
Ref Expression
strlem2
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem strlem2
StepHypRef Expression
1 fveq2 5720 . . . . 5
21fveq1d 5722 . . . 4
32fveq2d 5724 . . 3
43oveq1d 6088 . 2
5 strlem2.1 . 2
6 ovex 6098 . 2
74, 5, 6fvmpt 5798 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725   cmpt 4258  cfv 5446  (class class class)co 6073  c2 10041  cexp 11374  cno 22418  cch 22424   cpjh 22432 This theorem is referenced by:  strlem3a  23747  strlem4  23749  strlem5  23750  jplem2  23764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-iota 5410  df-fun 5448  df-fv 5454  df-ov 6076
 Copyright terms: Public domain W3C validator