Theorem nfcsb1 3917

Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)

Hypothesis

Ref	Expression
nfcsb1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfcsb1	⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Proof of Theorem nfcsb1

Step	Hyp	Ref	Expression
1		nfcsb1.1	. . . 4 ⊢ Ⅎ𝑥𝐴
2	1	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝐴)
3	2	nfcsb1d 3916	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1548	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1542  Ⅎwnfc 2883  ⦋csb 3893

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-nfc 2885  df-sbc 3778  df-csb 3894

This theorem is referenced by:  nfcsb1v  3918  fsumsplit1  15695  iundisj  25289  disjabrex  32068  disjabrexf  32069  iundisjf  32075  iundisjfi  32262  rdgssun  36562  disjinfi  44190  fsumsermpt  44594  climsubmpt  44675  climeldmeqmpt  44683  climfveqmpt  44686  climfveqmpt3  44697  climeldmeqmpt3  44704  climinf2mpt  44729  climinfmpt  44730  dvmptmulf  44952  dvnmptdivc  44953  sge0f1o  45397  sge0lempt  45425  sge0isummpt2  45447  meadjiun  45481  hoimbl2  45680  vonhoire  45687