![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ax12 | Structured version Visualization version GIF version |
Description: A weaker form of ax-12 2202 and ax12v2 2204, namely the generalization over 𝑥 of the latter. In this statement, all occurrences of 𝑥 are bound. (Contributed by BJ, 26-Dec-2020.) |
Ref | Expression |
---|---|
bj-ax12 | ⊢ ∀𝑥(𝑥 = 𝑡 → (𝜑 → ∀𝑥(𝑥 = 𝑡 → 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax12v2 2204 | . 2 ⊢ (𝑥 = 𝑡 → (𝜑 → ∀𝑥(𝑥 = 𝑡 → 𝜑))) | |
2 | 1 | ax-gen 1869 | 1 ⊢ ∀𝑥(𝑥 = 𝑡 → (𝜑 → ∀𝑥(𝑥 = 𝑡 → 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1628 |
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 1990 ax-6 2056 ax-7 2092 ax-12 2202 |
This theorem depends on definitions: df-bi 197 df-an 383 df-ex 1852 |
This theorem is referenced by: bj-ax12ssb 32967 bj-sb56 32970 |
Copyright terms: Public domain | W3C validator |