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Mirrors > Home > MPE Home > Th. List > ax12a2OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of ax12v 2035 as of 24-Mar-2021. (Contributed by NM, 12-Feb-2007.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax12a2OLD.1 | ⊢ (𝑥 = 𝑧 → (∀𝑧𝜑 → ∀𝑥(𝑥 = 𝑧 → 𝜑))) |
Ref | Expression |
---|---|
ax12a2OLD | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → (𝑥 = 𝑦 → (𝜑 → ∀𝑥(𝑥 = 𝑦 → 𝜑)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax12v 2035 | . 2 ⊢ (𝑥 = 𝑧 → (𝜑 → ∀𝑥(𝑥 = 𝑧 → 𝜑))) | |
2 | 1 | ax12v2OLD 2330 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → (𝑥 = 𝑦 → (𝜑 → ∀𝑥(𝑥 = 𝑦 → 𝜑)))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: axc15OLD 2332 |
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