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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 1407 1  |-  F/_ x [_ A  /  x ]_ B
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1399   F/_wnfc 2602   [_csb 3420
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-sbc 3325  df-csb 3421
This theorem is referenced by:  nfcsb1v  3436  iundisj  22124  disjabrex  27653  disjabrexf  27654  iundisjf  27659  iundisjfi  27835  fsumsplit1  31812  fprodsplit1f  31832  dvmptmulf  31973  dvnmptdivc  31974
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