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Mirrors > Home > ILE Home > Th. List > nfia1 | GIF version |
Description: Lemma 23 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) |
Ref | Expression |
---|---|
nfia1 | ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1474 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | nfa1 1474 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜓 | |
3 | 1, 2 | nfim 1504 | 1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1282 Ⅎwnf 1389 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-4 1440 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 |
This theorem is referenced by: (None) |
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