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| Mirrors > Home > MPE Home > Th. List > ax6evr | Structured version Visualization version GIF version | ||
| Description: A commuted form of ax6ev 1969. (Contributed by BJ, 7-Dec-2020.) |
| Ref | Expression |
|---|---|
| ax6evr | ⊢ ∃𝑥 𝑦 = 𝑥 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax6ev 1969 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
| 2 | equcomiv 2013 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
| 3 | 1, 2 | eximii 1837 | 1 ⊢ ∃𝑥 𝑦 = 𝑥 |
| Colors of variables: wff setvar class |
| Syntax hints: ∃wex 1779 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 |
| This theorem depends on definitions: df-bi 207 df-ex 1780 |
| This theorem is referenced by: ax7 2015 equvinva 2029 ax12v2 2179 19.8a 2181 axc11n 2431 mo4 2566 eu6lem 2573 axprlem3OLD 5428 dfid2 5580 relopabi 5832 relop 5861 bj-ax6e 36669 axc11n11r 36684 bj-dfid2ALT 37066 wl-spae 37522 sn-axprlem3 42256 ormkglobd 46890 |
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