Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-hbaeb | Structured version Visualization version GIF version |
Description: Biconditional version of hbae 2430. (Contributed by BJ, 6-Oct-2018.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-hbaeb | ⊢ (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑧∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-hbaeb2 34738 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥∀𝑧 𝑥 = 𝑦) | |
2 | alcom 2160 | . 2 ⊢ (∀𝑥∀𝑧 𝑥 = 𝑦 ↔ ∀𝑧∀𝑥 𝑥 = 𝑦) | |
3 | 1, 2 | bitri 278 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑧∀𝑥 𝑥 = 𝑦) |
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-5 1918 ax-6 1976 ax-7 2016 ax-10 2141 ax-11 2158 ax-12 2175 ax-13 2371 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-ex 1788 df-nf 1792 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |