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 2148 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | nfa1 2148 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜓 | |
3 | 1, 2 | nfim 1899 | 1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1537 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-10 2137 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-ex 1783 df-nf 1787 |
This theorem is referenced by: dfmoeu 2536 2eu6 2658 |
Copyright terms: Public domain | W3C validator |