Theorem relded 10624

Description: A deductive system is a relation.

Assertion

Ref	Expression
relded	|- Rel Ded

Proof of Theorem relded

Step	Hyp	Ref	Expression
1		strded 10623	. . 3 |- Ded (_ ((V X. V) X. (V X. V))
2		xpss 3227	. . 3 |- ((V X. V) X. (V X. V)) (_ (V X. V)
3	1, 2	sstri 2071	. 2 |- Ded (_ (V X. V)
4		df-rel 3182	. 2 |- (Rel Ded <-> Ded (_ (V X. V))
5	3, 4	mpbir 190	1 |- Rel Ded

Syntax hints:  Vcvv 1809   (_ wss 2045   X. cxp 3165  Rel wrel 3172  Dedcded 10618

This theorem is referenced by:  dedalg 10627

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-11 966  ax-12 967  ax-13 968  ax-14 969  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-sep 2700  ax-pow 2739  ax-pr 2776

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1172  df-eu 1382  df-mo 1383  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1586  df-v 1810  df-dif 2047  df-un 2048  df-in 2049  df-ss 2051  df-nul 2279  df-pw 2400  df-sn 2410  df-pr 2411  df-op 2414  df-opab 2664  df-xp 3181  df-rel 3182  df-ded 10619

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