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Theorem axnulALT 4328
 Description: Prove axnul 4329 directly from ax-rep 4312 using none of the equality axioms ax-8 1687 through ax-15 2219 provided we accept sp 1763 as an axiom. Replace sp 1763 with the obsolete ax-4 2211 to see this in 'show traceback'. (Contributed by Jeff Hoffman, 3-Feb-2008.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axnulALT
Distinct variable group:   ,

Proof of Theorem axnulALT
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-rep 4312 . . 3
2 sp 1763 . . . . . 6
32con2i 114 . . . . 5
4 df-ex 1551 . . . . 5
53, 4sylibr 204 . . . 4
6 fal 1331 . . . . . 6
7 sp 1763 . . . . . 6
86, 7mto 169 . . . . 5
98pm2.21i 125 . . . 4
105, 9mpg 1557 . . 3
111, 10mpg 1557 . 2
128intnan 881 . . . . . 6
1312nex 1564 . . . . 5
1413nbn 337 . . . 4
1514albii 1575 . . 3
1615exbii 1592 . 2
1711, 16mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   wfal 1326  wal 1549  wex 1550   wceq 1652   wcel 1725 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-11 1761  ax-rep 4312 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-fal 1329  df-ex 1551
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