nf3 - Metamath Proof Explorer

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Theorem nf3 1712

Description: Alternate definition of non-freeness. (Contributed by BJ, 16-Sep-2021.)

**Assertion**
Ref	Expression
nf3	$\/$

**Proof of Theorem nf3**
Step	Hyp	Ref	Expression
1		nf2 1711	. 2 $\/$
2		alnex 1706	. . 3
3	2	orbi2i 541	. 2 $\/$ $\/$
4	1, 3	bitr4i 267	1 $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wb 196 $\/$ wo 383

wal 1481

wex 1704

wnf 1708

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8

This theorem depends on definitions: df-bi 197 df-or 385 df-ex 1705 df-nf 1710

This theorem is referenced by: nf4 1713 nfntht2 1720 nfnbi 1781 nfntOLDOLD 1783 nfim1 2067