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Mirrors > Home > NFE Home > Th. List > iota4an | Unicode version |
Description: Theorem *14.23 in [WhiteheadRussell] p. 191. (Contributed by Andrew Salmon, 12-Jul-2011.) |
Ref | Expression |
---|---|
iota4an |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iota4 4357 | . 2 | |
2 | iotaex 4356 | . . . 4 | |
3 | simpl 443 | . . . . 5 | |
4 | 3 | sbcth 3060 | . . . 4 |
5 | 2, 4 | ax-mp 8 | . . 3 |
6 | sbcimg 3087 | . . . 4 | |
7 | 2, 6 | ax-mp 8 | . . 3 |
8 | 5, 7 | mpbi 199 | . 2 |
9 | 1, 8 | syl 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wcel 1710 weu 2204 cvv 2859 wsbc 3046 cio 4337 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-pr 3742 df-uni 3892 df-iota 4339 |
This theorem is referenced by: (None) |
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