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Mirrors > Home > MPE Home > Th. List > ax6evr | Structured version Visualization version GIF version |
Description: A commuted form of ax6ev 2054. (Contributed by BJ, 7-Dec-2020.) |
Ref | Expression |
---|---|
ax6evr | ⊢ ∃𝑥 𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6ev 2054 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
2 | equcomiv 2094 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
3 | 1, 2 | eximii 1911 | 1 ⊢ ∃𝑥 𝑦 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1851 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1869 ax-4 1884 ax-5 1986 ax-6 2052 ax-7 2088 |
This theorem depends on definitions: df-bi 197 df-ex 1852 |
This theorem is referenced by: ax7 2096 equviniva 2111 ax12v2 2196 19.8a 2197 axc11n 2449 euequ1 2611 relopabi 5399 relop 5426 bj-ax6e 32957 axc11n11r 32977 wl-spae 33617 |
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