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Mirrors > Home > NFE Home > Th. List > ifeq12 | Unicode version |
Description: Equality theorem for conditional operators. (Contributed by NM, 1-Sep-2004.) |
Ref | Expression |
---|---|
ifeq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifeq1 3667 | . 2 | |
2 | ifeq2 3668 | . 2 | |
3 | 1, 2 | sylan9eq 2405 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wceq 1642 cif 3663 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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 |
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-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-rab 2624 df-v 2862 df-nin 3212 df-compl 3213 df-un 3215 df-if 3664 |
This theorem is referenced by: (None) |
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