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Mirrors > Home > ILE Home > Th. List > nfralw | Unicode version |
Description: Bound-variable hypothesis builder for restricted quantification. See nfralya 2510 for a version with and distinct instead of and . (Contributed by NM, 1-Sep-1999.) (Revised by Gino Giotto, 10-Jan-2024.) |
Ref | Expression |
---|---|
nfralw.1 | |
nfralw.2 |
Ref | Expression |
---|---|
nfralw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1459 | . . 3 | |
2 | nfralw.1 | . . . 4 | |
3 | 2 | a1i 9 | . . 3 |
4 | nfralw.2 | . . . 4 | |
5 | 4 | a1i 9 | . . 3 |
6 | 1, 3, 5 | nfraldw 2502 | . 2 |
7 | 6 | mptru 1357 | 1 |
Colors of variables: wff set class |
Syntax hints: wtru 1349 wnf 1453 wnfc 2299 wral 2448 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 |
This theorem is referenced by: rspc2vd 3117 fprod2dlemstep 11578 fprodcom2fi 11582 nnwofdc 11986 |
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