Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > wfis2 | Structured version Visualization version Unicode version |
Description: Well Founded Induction schema, using implicit substitution. (Contributed by Scott Fenton, 29-Jan-2011.) |
Ref | Expression |
---|---|
wfis2.1 | |
wfis2.2 | Se |
wfis2.3 | |
wfis2.4 |
Ref | Expression |
---|---|
wfis2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wfis2.1 | . . 3 | |
2 | wfis2.2 | . . 3 Se | |
3 | wfis2.3 | . . . 4 | |
4 | wfis2.4 | . . . 4 | |
5 | 3, 4 | wfis2g 5719 | . . 3 Se |
6 | 1, 2, 5 | mp2an 708 | . 2 |
7 | 6 | rspec 2931 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wcel 1990 wral 2912 Se wse 5071 wwe 5072 cpred 5679 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-po 5035 df-so 5036 df-fr 5073 df-se 5074 df-we 5075 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 |
This theorem is referenced by: wfis3 5721 |
Copyright terms: Public domain | W3C validator |