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Theorem nfcsb 3907
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfcsb.1 𝑥𝐴
nfcsb.2 𝑥𝐵
Assertion
Ref Expression
nfcsb 𝑥𝐴 / 𝑦𝐵

Proof of Theorem nfcsb
StepHypRef Expression
1 nftru 1796 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 11 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 3905 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76mptru 1535 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff setvar class
Syntax hints:  wtru 1529  wnfc 2958  csb 3880
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-13 2381  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-sbc 3770  df-csb 3881
This theorem is referenced by:  cbvralcsf  3922  cbvreucsf  3924  cbvrabcsf  3925  elfvmptrab1  6787  elovmporab1  7382  nfsum  15036
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