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Theorem nfcsb1 3514
 Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfcsb1.1 𝑥𝐴
Assertion
Ref Expression
nfcsb1 𝑥𝐴 / 𝑥𝐵

Proof of Theorem nfcsb1
StepHypRef Expression
1 nfcsb1.1 . . . 4 𝑥𝐴
21a1i 11 . . 3 (⊤ → 𝑥𝐴)
32nfcsb1d 3513 . 2 (⊤ → 𝑥𝐴 / 𝑥𝐵)
43trud 1484 1 𝑥𝐴 / 𝑥𝐵
 Colors of variables: wff setvar class Syntax hints:  ⊤wtru 1476  Ⅎwnfc 2738  ⦋csb 3499 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-sbc 3403  df-csb 3500 This theorem is referenced by:  nfcsb1v  3515  fprodsplit1f  14560  iundisj  23123  disjabrex  28777  disjabrexf  28778  iundisjf  28784  iundisjfi  28942  disjinfi  38375  fsumsplit1  38639  fsumsermpt  38646  climsubmpt  38727  climeldmeqmpt  38735  climfveqmpt  38738  dvmptmulf  38827  dvnmptdivc  38828  sge0f1o  39275  sge0lempt  39303  sge0isummpt2  39325  meadjiun  39359  hoimbl2  39555  vonhoire  39563
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