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Mirrors > Home > ILE Home > Th. List > 19.17 | GIF version |
Description: Theorem 19.17 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
19.17.1 | ⊢ Ⅎ𝑥𝜓 |
Ref | Expression |
---|---|
19.17 | ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∀𝑥𝜑 ↔ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | albi 1357 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓)) | |
2 | 19.17.1 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
3 | 2 | 19.3 1446 | . 2 ⊢ (∀𝑥𝜓 ↔ 𝜓) |
4 | 1, 3 | syl6bb 185 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∀𝑥𝜑 ↔ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 98 ∀wal 1241 Ⅎwnf 1349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-4 1400 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: (None) |
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