Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ax9lem5 Unicode version

Theorem ax9lem5 29144
 Description: Lemma for ax9 1889. Similar to spim 1915 with distinct variables, without using sp 1716, ax9 1889, or ax10 1884. (Contributed by NM, 7-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ax9lem5.a
ax9lem5.c
ax9lem5.d
ax9lem5.2
ax9lem5.3
Assertion
Ref Expression
ax9lem5
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,)   (,)

Proof of Theorem ax9lem5
StepHypRef Expression
1 ax9lem5.3 . . . . 5
21com12 27 . . . 4
3 ax9lem5.2 . . . 4
42, 3syl6 29 . . 3
54alimi 1546 . 2
6 ax9lem5.a . . 3
7 ax9lem5.c . . 3
8 ax9lem5.d . . 3
96, 7, 8ax9lem4 29143 . 2
105, 9syl 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1527 This theorem is referenced by:  ax9lem6  29145 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-8 1643  ax-6 1703  ax-11 1715
 Copyright terms: Public domain W3C validator