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Theorem bj-stand 12945
 Description: The conjunction of two stable formulas is stable. Deduction form of bj-stan 12944. Its proof is shorter, so one could prove it first and then bj-stan 12944 from it, the usual way. (Contributed by BJ, 24-Nov-2023.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-stand.1 STAB
bj-stand.2 STAB
Assertion
Ref Expression
bj-stand STAB

Proof of Theorem bj-stand
StepHypRef Expression
1 bj-nnan 12937 . . 3
2 bj-stand.1 . . . . 5 STAB
3 df-stab 816 . . . . 5 STAB
42, 3sylib 121 . . . 4
5 bj-stand.2 . . . . 5 STAB
6 df-stab 816 . . . . 5 STAB
75, 6sylib 121 . . . 4
84, 7anim12d 333 . . 3
91, 8syl5 32 . 2
10 df-stab 816 . 2 STAB
119, 10sylibr 133 1 STAB
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103  STAB wstab 815 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604 This theorem depends on definitions:  df-bi 116  df-stab 816 This theorem is referenced by: (None)
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