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Mirrors > Home > ILE Home > Th. List > spcgv | Unicode version |
Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 22-Jun-1994.) |
Ref | Expression |
---|---|
spcgv.1 |
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Ref | Expression |
---|---|
spcgv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2319 |
. 2
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2 | nfv 1528 |
. 2
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3 | spcgv.1 |
. 2
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4 | 1, 2, 3 | spcgf 2821 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2741 |
This theorem is referenced by: spcv 2833 mob2 2919 intss1 3861 dfiin2g 3921 exmidsssnc 4205 exmid1stab 4210 frirrg 4352 frind 4354 alxfr 4463 elirr 4542 en2lp 4555 tfisi 4588 mptfvex 5604 tfrcl 6368 rdgisucinc 6389 frecabex 6402 fisseneq 6934 mkvprop 7159 exmidfodomrlemr 7204 exmidfodomrlemrALT 7205 acfun 7209 exmidmotap 7263 ccfunen 7266 zfz1isolem1 10823 zfz1iso 10824 uniopn 13662 pw1nct 14914 sbthom 14936 |
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