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Theorem uncompl 4074

Description: Union with complement. (Contributed by SF, 2-Jan-2018.)

**Assertion**
Ref	Expression
uncompl	⊢ (A ∪ ∼ A) = V

**Proof of Theorem uncompl**
Step	Hyp	Ref	Expression
1		df-un 3214	. 2 ⊢ (A ∪ ∼ A) = ( ∼ A ⩃ ∼ ∼ A)
2		nincompl 4072	. 2 ⊢ ( ∼ A ⩃ ∼ ∼ A) = V
3	1, 2	eqtri 2373	1 ⊢ (A ∪ ∼ A) = V

Colors of variables: wff setvar class

Syntax hints: = wceq 1642 Vcvv 2859 ⩃ cnin 3204 ∼ ccompl 3205 ∪ cun 3207

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214

This theorem is referenced by: ssofss 4076 vvex 4109 vfintle 4546 vfin1cltv 4547 fnfullfun 5858