![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > ax6evr | Structured version Visualization version GIF version |
Description: A commuted form of ax6ev 1974. (Contributed by BJ, 7-Dec-2020.) |
Ref | Expression |
---|---|
ax6evr | ⊢ ∃𝑥 𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6ev 1974 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
2 | equcomiv 2018 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
3 | 1, 2 | eximii 1840 | 1 ⊢ ∃𝑥 𝑦 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 |
This theorem depends on definitions: df-bi 206 df-ex 1783 |
This theorem is referenced by: ax7 2020 equvinva 2034 ax12v2 2174 19.8a 2175 axc11n 2426 mo4 2561 eu6lem 2568 axprlem3 5424 dfid2 5577 relopabi 5823 relop 5851 bj-ax6e 35545 axc11n11r 35561 bj-dfid2ALT 35946 wl-spae 36390 sn-axprlem3 41034 |
Copyright terms: Public domain | W3C validator |