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Mirrors > Home > MPE Home > Th. List > psseq1 | Structured version Visualization version Unicode version |
Description: Equality theorem for proper subclass. (Contributed by NM, 7-Feb-1996.) |
Ref | Expression |
---|---|
psseq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1 3626 | . . 3 | |
2 | neeq1 2856 | . . 3 | |
3 | 1, 2 | anbi12d 747 | . 2 |
4 | df-pss 3590 | . 2 | |
5 | df-pss 3590 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 303 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wne 2794 wss 3574 wpss 3575 |
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-ne 2795 df-in 3581 df-ss 3588 df-pss 3590 |
This theorem is referenced by: psseq1i 3696 psseq1d 3699 psstr 3711 sspsstr 3712 brrpssg 6939 sorpssuni 6946 pssnn 8178 marypha1lem 8339 infeq5i 8533 infpss 9039 fin4i 9120 isfin2-2 9141 zornn0g 9327 ttukeylem7 9337 elnp 9809 elnpi 9810 ltprord 9852 pgpfac1lem1 18473 pgpfac1lem5 18478 pgpfac1 18479 pgpfaclem2 18481 pgpfac 18483 islbs3 19155 alexsubALTlem4 21854 wilthlem2 24795 spansncv 28512 cvbr 29141 cvcon3 29143 cvnbtwn 29145 dfon2lem3 31690 dfon2lem4 31691 dfon2lem5 31692 dfon2lem6 31693 dfon2lem7 31694 dfon2lem8 31695 dfon2 31697 lcvbr 34308 lcvnbtwn 34312 mapdcv 36949 |
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