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Theorem nfcsb 3817
Description: Bound-variable hypothesis builder for substitution into a class. Usage of this theorem is discouraged because it depends on ax-13 2372. Use the weaker nfcsbw 3816 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 1811 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 11 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 3815 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76mptru 1549 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff setvar class
Syntax hints:  wtru 1543  wnfc 2879  csb 3790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2162  ax-12 2179  ax-13 2372  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-ex 1787  df-nf 1791  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-nfc 2881  df-sbc 3681  df-csb 3791
This theorem is referenced by:  cbvralcsf  3832  cbvreucsf  3834  cbvrabcsf  3835  elfvmptrab1  6802  elovmporab1  7409  nfsumOLD  15141
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