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Theorem nfcsb 3920
Description: Bound-variable hypothesis builder for substitution into a class. Usage of this theorem is discouraged because it depends on ax-13 2367. Use the weaker nfcsbw 3919 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 1799 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 11 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 3918 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76mptru 1541 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff setvar class
Syntax hints:  wtru 1535  wnfc 2879  csb 3892
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-13 2367  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-sbc 3777  df-csb 3893
This theorem is referenced by:  cbvralcsf  3937  cbvreucsf  3939  cbvrabcsf  3940  elfvmptrab1  7033  elovmporab1  7669
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