Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > nfia1 | Structured version Visualization version 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 2015 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | nfa1 2015 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜓 | |
3 | 1, 2 | nfim 1813 | 1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 Ⅎwnf 1699 |
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-10 2006 |
This theorem depends on definitions: df-bi 196 df-or 384 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: mo2v 2465 2eu6 2546 |
Copyright terms: Public domain | W3C validator |