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Mirrors > Home > MPE Home > Th. List > ax6evr | Structured version Visualization version GIF version |
Description: A commuted form of ax6ev 1972. (Contributed by BJ, 7-Dec-2020.) |
Ref | Expression |
---|---|
ax6evr | ⊢ ∃𝑥 𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6ev 1972 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
2 | equcomiv 2021 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
3 | 1, 2 | eximii 1837 | 1 ⊢ ∃𝑥 𝑦 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 |
This theorem depends on definitions: df-bi 209 df-ex 1781 |
This theorem is referenced by: ax7 2023 equvinva 2037 ax12v2 2179 19.8a 2180 axc11n 2448 mo4 2650 eu6lem 2658 axprlem3 5326 relopabi 5694 relop 5721 bj-ax6e 34001 axc11n11r 34017 wl-spae 34776 sn-axprlem3 39129 |
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