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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ax12wlem | Structured version Visualization version GIF version |
Description: A lemma used to prove a weak version of the axiom of substitution ax-12 2179. (Temporary comment: The general statement that ax12wlem 2136 proves.) (Contributed by BJ, 20-Mar-2020.) |
Ref | Expression |
---|---|
bj-ax12wlem.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
bj-ax12wlem | ⊢ (𝜑 → (𝜓 → ∀𝑥(𝜑 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-ax12wlem.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | ax-5 1917 | . 2 ⊢ (𝜒 → ∀𝑥𝜒) | |
3 | 1, 2 | bj-ax12i 34461 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥(𝜑 → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 |
This theorem depends on definitions: df-bi 210 df-an 400 |
This theorem is referenced by: bj-ax12w 34501 |
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