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Theorem nfel2 2501
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)
Hypothesis
Ref Expression
nfeq2.1 xB
Assertion
Ref Expression
nfel2 x A B
Distinct variable group:   x,A
Allowed substitution hint:   B(x)

Proof of Theorem nfel2
StepHypRef Expression
1 nfcv 2489 . 2 xA
2 nfeq2.1 . 2 xB
31, 2nfel 2497 1 x A B
Colors of variables: wff setvar class
Syntax hints:  wnf 1544   wcel 1710  wnfc 2476
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 2478
This theorem is referenced by:  elabgt  2982  nfnin  3228  opelopabsb  4697  eliunxp  4821  opeliunxp2  4822  iunxpf  4829
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