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Theorem nfcsb1 3435
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfcsb1.1  |-  F/_ x A
Assertion
Ref Expression
nfcsb1  |-  F/_ x [_ A  /  x ]_ B

Proof of Theorem nfcsb1
StepHypRef Expression
1 nfcsb1.1 . . . 4  |-  F/_ x A
21a1i 11 . . 3  |-  ( T. 
->  F/_ x A )
32nfcsb1d 3434 . 2  |-  ( T. 
->  F/_ x [_ A  /  x ]_ B )
43trud 1392 1  |-  F/_ x [_ A  /  x ]_ B
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1384   F/_wnfc 2591   [_csb 3420
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-sbc 3314  df-csb 3421
This theorem is referenced by:  nfcsb1v  3436  iundisj  21831  disjabrex  27315  disjabrexf  27316  iundisjf  27320  iundisjfi  27473
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