Theorem nfel2 2502

Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
nfeq2.1	⊢ ℲxB

Assertion

Ref	Expression
nfel2	⊢ Ⅎx A ∈ B

Distinct variable group:   x,A

Allowed substitution hint:   B(x)

Proof of Theorem nfel2

Step	Hyp	Ref	Expression
1		nfcv 2490	. 2 ⊢ ℲxA
2		nfeq2.1	. 2 ⊢ ℲxB
3	1, 2	nfel 2498	1 ⊢ Ⅎx A ∈ B

Syntax hints:  Ⅎwnf 1544   ∈ wcel 1710  Ⅎwnfc 2477

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2479

This theorem is referenced by:  elabgt  2983  nfnin  3229  opelopabsb  4698  eliunxp  4822  opeliunxp2  4823  iunxpf  4830