Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > alrot3 | Structured version Visualization version GIF version |
Description: Theorem *11.21 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.) |
Ref | Expression |
---|---|
alrot3 | ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 2160 | . 2 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑥∀𝑧𝜑) | |
2 | alcom 2160 | . . 3 ⊢ (∀𝑥∀𝑧𝜑 ↔ ∀𝑧∀𝑥𝜑) | |
3 | 2 | albii 1827 | . 2 ⊢ (∀𝑦∀𝑥∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑) |
4 | 1, 3 | bitri 278 | 1 ⊢ (∀𝑥∀𝑦∀𝑧𝜑 ↔ ∀𝑦∀𝑧∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ∀wal 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-11 2158 |
This theorem depends on definitions: df-bi 210 |
This theorem is referenced by: alrot4 2162 nfnid 5268 raliunxp 5708 dff13 7067 cosscnvssid3 36331 undmrnresiss 40888 |
Copyright terms: Public domain | W3C validator |