Theorem difexi 4252

Description: Existence of a difference, inference version of difexg 4251. (Contributed by Glauco Siliprandi, 3-Mar-2021.) (Revised by AV, 26-Mar-2021.)

Hypothesis

Ref	Expression
difexi.1	|- A e. _V

Assertion

Ref	Expression
difexi	|- ( A \ B ) e. _V

Proof of Theorem difexi

Step	Hyp	Ref	Expression
1		difexi.1	. 2 |- A e. _V
2		difexg 4251	. 2 |- ( A e. _V -> ( A \ B ) e. _V )
3	1, 2	ax-mp 5	1 |- ( A \ B ) e. _V

Syntax hints:   e. wcel 2203   _Vcvv 2812   \ cdif 3207

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214  ax-sep 4227

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-v 2814  df-dif 3212  df-in 3216  df-ss 3223

This theorem is referenced by:  hashfibclem  11199