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Theorem rint0 3966
 Description: Relative intersection of an empty set. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
rint0 (X = → (AX) = A)

Proof of Theorem rint0
StepHypRef Expression
1 inteq 3929 . . 3 (X = X = )
21ineq2d 3457 . 2 (X = → (AX) = (A))
3 int0 3940 . . . 4 = V
43ineq2i 3454 . . 3 (A) = (A ∩ V)
5 inv1 3577 . . 3 (A ∩ V) = A
64, 5eqtri 2373 . 2 (A) = A
72, 6syl6eq 2401 1 (X = → (AX) = A)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  Vcvv 2859   ∩ cin 3208  ∅c0 3550  ∩cint 3926 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551  df-int 3927 This theorem is referenced by: (None)
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