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Mirrors > Home > MPE Home > Th. List > 19.3vOLD | Structured version Visualization version GIF version |
Description: Obsolete version of 19.3v 1985 as of 20-Oct-2023. (Contributed by Anthony Hart, 13-Sep-2011.) Remove dependency on ax-7 2014. (Revised by Wolf Lammen, 4-Dec-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
19.3vOLD | ⊢ (∀𝑥𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alex 1825 | . 2 ⊢ (∀𝑥𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑) | |
2 | 19.9v 1987 | . . 3 ⊢ (∃𝑥 ¬ 𝜑 ↔ ¬ 𝜑) | |
3 | 2 | con2bii 360 | . 2 ⊢ (𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑) |
4 | 1, 3 | bitr4i 280 | 1 ⊢ (∀𝑥𝜑 ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 208 ∀wal 1534 ∃wex 1779 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 |
This theorem depends on definitions: df-bi 209 df-ex 1780 |
This theorem is referenced by: (None) |
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