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Theorem nfcsb 3925
Description: Bound-variable hypothesis builder for substitution into a class. Usage of this theorem is discouraged because it depends on ax-13 2376. Use the weaker nfcsbw 3924 when possible. (Contributed by Mario Carneiro, 12-Oct-2016.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfcsb.1 𝑥𝐴
nfcsb.2 𝑥𝐵
Assertion
Ref Expression
nfcsb 𝑥𝐴 / 𝑦𝐵

Proof of Theorem nfcsb
StepHypRef Expression
1 nftru 1803 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 11 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 3923 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76mptru 1546 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff setvar class
Syntax hints:  wtru 1540  wnfc 2889  csb 3898
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-10 2140  ax-11 2156  ax-12 2176  ax-13 2376  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-nf 1783  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-sbc 3788  df-csb 3899
This theorem is referenced by:  cbvralcsf  3940  cbvreucsf  3942  cbvrabcsf  3943  elfvmptrab1  7043  elovmporab1  7682
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