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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-abeq1 | Structured version Visualization version Unicode version |
Description: Remove dependency on ax-13 2246 from abeq1 2733. Remark: the theorems abeq2i 2735, abeq1i 2736, abeq2d 2734 do not use ax-11 2034 or ax-13 2246. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-abeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-abeq2 32773 | . 2 | |
2 | eqcom 2629 | . 2 | |
3 | bicom 212 | . . 3 | |
4 | 3 | albii 1747 | . 2 |
5 | 1, 2, 4 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wal 1481 wceq 1483 wcel 1990 cab 2608 |
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-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 |
This theorem is referenced by: (None) |
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