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Theorem bj-ssbequ1 31321
 Description: This uses ax-12 1950 with a direct reference to ax12v 1951. Therefore, compared to bj-ax12 31311, there is a hidden use of sp 1957. Note that with ax-12 1950, it can be proved with dv condition on . See sbequ1 2097. (Contributed by BJ, 22-Dec-2020.)
Assertion
Ref Expression
bj-ssbequ1 [/]b

Proof of Theorem bj-ssbequ1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 equtr2 1877 . . . . . . . 8
21equcomd 1871 . . . . . . 7
3 ax12v 1951 . . . . . . 7
42, 3syl 17 . . . . . 6
54expimpd 614 . . . . 5
65com12 31 . . . 4
76alrimiv 1781 . . 3
87ex 441 . 2
9 df-ssb 31297 . 2 [/]b
108, 9syl6ibr 235 1 [/]b
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376  wal 1450  [wssb 31296 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-ssb 31297 This theorem is referenced by:  bj-ssbid1  31324
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