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Mirrors > Home > MPE Home > Th. List > ax9v2 | Structured version Visualization version GIF version |
Description: Second of two weakened versions of ax9v 1987, with an extra dv condition on 𝑦, 𝑧 see comments there. (Contributed by BJ, 7-Dec-2020.) |
Ref | Expression |
---|---|
ax9v2 | ⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax9v 1987 | 1 ⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-9 1986 |
This theorem is referenced by: ax9 1990 |
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