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Mirrors > Home > MPE Home > Th. List > preqsnOLD | Structured version Visualization version Unicode version |
Description: Obsolete proof of preqsn 4393 as of 23-Jul-2021. (Contributed by NM, 3-Jun-2008.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
preqsn.1 | |
preqsn.2 | |
preqsn.3 |
Ref | Expression |
---|---|
preqsnOLD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 4190 | . . 3 | |
2 | 1 | eqeq2i 2634 | . 2 |
3 | preqsn.1 | . . . 4 | |
4 | preqsn.2 | . . . 4 | |
5 | preqsn.3 | . . . 4 | |
6 | 3, 4, 5, 5 | preq12b 4382 | . . 3 |
7 | oridm 536 | . . . 4 | |
8 | eqtr3 2643 | . . . . . 6 | |
9 | simpr 477 | . . . . . 6 | |
10 | 8, 9 | jca 554 | . . . . 5 |
11 | eqtr 2641 | . . . . . 6 | |
12 | simpr 477 | . . . . . 6 | |
13 | 11, 12 | jca 554 | . . . . 5 |
14 | 10, 13 | impbii 199 | . . . 4 |
15 | 7, 14 | bitri 264 | . . 3 |
16 | 6, 15 | bitri 264 | . 2 |
17 | 2, 16 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wo 383 wa 384 wceq 1483 wcel 1990 cvv 3200 csn 4177 cpr 4179 |
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-v 3202 df-un 3579 df-sn 4178 df-pr 4180 |
This theorem is referenced by: (None) |
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