Theorem ral0 2362

Description: Vacuous universal quantification is always true.

Assertion

Ref	Expression
ral0	|- A.x e. (/) ph

Proof of Theorem ral0

Step	Hyp	Ref	Expression
1		noel 2287	. . 3 |- -. x e. (/)
2	1	pm2.21i 77	. 2 |- (x e. (/) -> ph)
3	2	rgen 1701	1 |- A.x e. (/) ph

Syntax hints:   e. wcel 960  A.wral 1648  (/)c0 2283

This theorem is referenced by:  0iin 2610  ixp0x 4365  xrsupsslem 6078  xrinfmsslem 6079  xrsup0 6099  0met 7822  chocnul 9287  emhgrat 10746

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-ral 1652  df-v 1815  df-dif 2052  df-nul 2284

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