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Theorem spimt 1946
 Description: Closed theorem form of spim 1947. (Contributed by NM, 15-Jan-2008.) (Revised by Mario Carneiro, 17-Oct-2016.)
Assertion
Ref Expression
spimt

Proof of Theorem spimt
StepHypRef Expression
1 nfnf1 1780 . . . . 5
2 nfa1 1779 . . . . 5
31, 2nfan 1800 . . . 4
4 sp 1733 . . . . . . 7
54adantl 452 . . . . . 6
6 nfr 1765 . . . . . . 7
76adantr 451 . . . . . 6
85, 7embantd 50 . . . . 5
98imim2d 48 . . . 4
103, 9alimd 1768 . . 3
1110impancom 427 . 2
12 ax9o 1922 . 2
1311, 12syl6 29 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1531  wnf 1535 This theorem is referenced by:  spim  1947  equveli  1960  a12lem1  28948 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536
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