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Mirrors > Home > MPE Home > Th. List > sb8 | Structured version Visualization version Unicode version |
Description: Substitution of variable in universal quantifier. (Contributed by NM, 16-May-1993.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Jim Kingdon, 15-Jan-2018.) |
Ref | Expression |
---|---|
sb5rf.1 |
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Ref | Expression |
---|---|
sb8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb5rf.1 |
. 2
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2 | 1 | nfs1 2194 |
. 2
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3 | sbequ12 2083 |
. 2
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4 | 1, 2, 3 | cbval 2114 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1664 df-nf 1668 df-sb 1798 |
This theorem is referenced by: sbhb 2267 sbnf2 2268 sb8eu 2332 sb8iota 5553 mo5f 28120 ax11-pm2 31438 bj-nfcf 31527 wl-sb8eut 31906 sbcalf 32352 |
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