Theorem nfcsb1 3882

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 3881	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1547	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1541  Ⅎwnfc 2876  ⦋csb 3859

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-nfc 2878  df-sbc 3751  df-csb 3860

This theorem is referenced by:  nfcsb1v  3883  fsumsplit1  15688  iundisj  25483  disjabrex  32562  disjabrexf  32563  iundisjf  32569  iundisjfi  32770  rdgssun  37360  evl1gprodd  42099  disjinfi  45180  fsumsermpt  45571  climsubmpt  45652  climeldmeqmpt  45660  climfveqmpt  45663  climfveqmpt3  45674  climeldmeqmpt3  45681  climinf2mpt  45706  climinfmpt  45707  dvmptmulf  45929  dvnmptdivc  45930  sge0lempt  46402  sge0isummpt2  46424  meadjiun  46458  hoimbl2  46657  vonhoire  46664