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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-equsal | Structured version Visualization version Unicode version |
Description: A useful equivalence related to substitution. (Contributed by NM, 2-Jun-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Revised by Mario Carneiro, 3-Oct-2016.) It seems proving wl-equsald 33325 first, and then deriving more specialized versions wl-equsal 33326 and wl-equsal1t 33327 then is more efficient than the other way round, which is possible, too. See also equsal 2291. (Revised by Wolf Lammen, 27-Jul-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
wl-equsal.1 | |
wl-equsal.2 |
Ref | Expression |
---|---|
wl-equsal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1730 | . . 3 | |
2 | wl-equsal.1 | . . . 4 | |
3 | 2 | a1i 11 | . . 3 |
4 | wl-equsal.2 | . . . 4 | |
5 | 4 | a1i 11 | . . 3 |
6 | 1, 3, 5 | wl-equsald 33325 | . 2 |
7 | 6 | trud 1493 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wtru 1484 wnf 1708 |
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-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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