Theorem ral0 2354

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 2280	. . 3 |- -. x e. (/)
2	1	pm2.21i 77	. 2 |- (x e. (/) -> ph)
3	2	rgen 1695	1 |- A.x e. (/) ph

Syntax hints:   e. wcel 956  A.wral 1642  (/)c0 2276

This theorem is referenced by:  0iin 2601  ixp0x 4349  xrsupsslem 6031  xrinfmsslem 6032  xrsup0 6052  0met 7777  chocnul 9230  emhgrat 10647

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-ral 1646  df-v 1808  df-dif 2045  df-nul 2277

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