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Mirrors > Home > MPE Home > Th. List > Mathboxes > alrimii | Structured version Visualization version Unicode version |
Description: A lemma for introducing a universal quantifier, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.) |
Ref | Expression |
---|---|
alrimii.1 | |
alrimii.2 | |
alrimii.3 | |
alrimii.4 |
Ref | Expression |
---|---|
alrimii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimii.1 | . . 3 | |
2 | alrimii.2 | . . . 4 | |
3 | alrimii.3 | . . . 4 | |
4 | 2, 3 | sylibr 224 | . . 3 |
5 | 1, 4 | alrimi 2082 | . 2 |
6 | nfsbc1v 3455 | . . 3 | |
7 | alrimii.4 | . . 3 | |
8 | sbceq2a 3447 | . . 3 | |
9 | 6, 7, 8 | cbval 2271 | . 2 |
10 | 5, 9 | sylib 208 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wnf 1708 wsbc 3435 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-sbc 3436 |
This theorem is referenced by: (None) |
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