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Theorem nfcsb1 3404
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 3403 . 2  |-  ( T. 
->  F/_ x [_ A  /  x ]_ B )
43trud 1379 1  |-  F/_ x [_ A  /  x ]_ B
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1371   F/_wnfc 2599   [_csb 3389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-sbc 3288  df-csb 3390
This theorem is referenced by:  nfcsb1v  3405  iundisj  21155  disjabrex  26070  disjabrexf  26071  iundisjf  26075  disjunsn  26080  f1od2  26168  iundisjfi  26218
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