Definition df-pred 6322

Description: Define the predecessor class of a binary relation. This is the class of all elements 𝑦 of 𝐴 such that 𝑦𝑅𝑋 (see elpred 6339). (Contributed by Scott Fenton, 29-Jan-2011.)

Assertion

Ref	Expression
df-pred	⊢ Pred(𝑅, 𝐴, 𝑋) = (𝐴 ∩ (◡𝑅 “ {𝑋}))

Detailed syntax breakdown of Definition df-pred

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cR	. . 3 class 𝑅
3		cX	. . 3 class 𝑋
4	1, 2, 3	cpred 6321	. 2 class Pred(𝑅, 𝐴, 𝑋)
5	2	ccnv 5687	. . . 4 class ◡𝑅
6	3	csn 4630	. . . 4 class {𝑋}
7	5, 6	cima 5691	. . 3 class (◡𝑅 “ {𝑋})
8	1, 7	cin 3961	. 2 class (𝐴 ∩ (◡𝑅 “ {𝑋}))
9	4, 8	wceq 1536	1 wff Pred(𝑅, 𝐴, 𝑋) = (𝐴 ∩ (◡𝑅 “ {𝑋}))

This definition is referenced by:  predeq123  6323  nfpred  6327  csbpredg  6328  predpredss  6329  predss  6330  sspred  6331  dfpred2  6332  elpredgg  6335  predexg  6340  dffr4  6342  predel  6343  predidm  6348  predin  6349  predun  6350  preddif  6351  predep  6352  pred0  6357  dfse3  6358  predrelss  6359  predprc  6360  predres  6361  frpoind  6364  wfiOLD  6373  frind  9787