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Theorem ax9sep 29212
 Description: Show that the Separation Axiom ax-sep 4220 and Extensionality ax-ext 2339 implies ax9 1954. Note that ax9 1954 and sp 1748 (which can be derived from ax9 1954) are not used by the proof. (Contributed by NM, 12-Nov-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax9sep

Proof of Theorem ax9sep
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax9vsep 4224 . 2
2 ax9vsep 4224 . 2
3 ax9vsep 4224 . 2
4 ax9vsep 4224 . 2
5 ax9vsep 4224 . 2
6 ax9vsep 4224 . 2
7 ax9vsep 4224 . 2
8 ax9vsep 4224 . 2
9 ax9vsep 4224 . 2
10 ax9vsep 4224 . 2
11 ax9vsep 4224 . 2
12 ax9vsep 4224 . 2
13 ax9vsep 4224 . 2
141, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13ax9vax9 29210 1
 Colors of variables: wff set class Syntax hints:   wn 3  wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
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